Novel heterogeneous neuron memristor coupling model and circuit

Abstract

The invention discloses a novel heterogeneous neuron memristor coupling model and circuit. A resistor, a capacitor, a triode, an operational amplifier, a multiplier, a direct current voltage source and a direct current source construct five circuit paths, namely a hyperbolic tangent simulation equivalent circuit and a hyperbolic tangent memristor simulation equivalent circuit. The calculation result of the coupling network shows that the network does not have a balance point, and the network shows hidden dynamic behaviors. The coupling network can generate five stable discharge modes such as periodic peak, chaotic peak, random bursting, chaotic bursting and periodic bursting. Due to the fact that different discharging modes can control the system to show different behavior modes, the circuit has important value for development of a bionic system.

Description

Technical Field

[0001] The present invention belongs to the technical field of heterogeneous neuron memristor coupling systems, and relates to a system model for realizing neuron heterogeneous coupling through memristors, and specifically to a construction method and circuit implementation of a novel heterogeneous neuron memristor coupling model. Technical Background

[0002] Neurons play an important role in the life activities of organisms. The information transmission between different neurons and between neurons and other cells and tissues is mainly completed through the membrane potential on neurons. External neurons are triggered to various states by generating various discharge signals, thereby directing the human body to perform various physiological activities. Some existing neuron models include Hindmarsh-Rose neurons, Hopfield neural networks, and many other neuron models.

[0003] Memristor, as the fourth basic electronic component, describes the relationship between charge and flux. Due to its nanometer size, memorability, nonlinearity and excellent biomimetic properties, many researchers have introduced it into neural networks as synapses or autosynapses.

[0004] There are many neurons in the biological brain, and their types are complex. Different brain regions in the brain or between brain regions and external neurons need to transmit information, and this process often involves different types of neurons. Using memristors to perform synaptic coupling of heterogeneous neurons can simulate signal transmission in different functional areas of the brain. At present, there is a lack of models and circuits for heterogeneously coupling Hindmarsh-Rose neurons and Hopfield neural networks through memristors, which is a shortcoming of the existing technology. Moreover, with the rise of brain-like intelligence and bionic system research, this model and circuit will also contribute to the development of bionic systems. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention proposes a novel heterogeneous neuron memristor coupling model and circuit.

[0006] 1. A novel heterogeneous neuron memristor coupling model and circuit construction method, characterized by comprising the following steps:

[0007] (1) Mathematical model of the hyperbolic tangent memristor designed in the present invention:

[0008]

[0009] Where v and i represent the input voltage and output current of the memristor, t is the time constant, x is the internal magnetic flux of the memristor, k1 and c are two internal parameters of the memristor, and c = 0.01.

[0010] (2) The two-dimensional Hindmarsh-Rose neuron model is:

[0011]

[0012] Where x and y represent the potential on the neuron cell membrane and the related recovery variable respectively, I is the external stimulation current, a, b, c, d are the internal parameters related to the neuron, a=1, b=3, c=1, d=5, I=0.

[0013] (3) The mathematical model of the Hopfield neural network is:

[0014]

[0015] Among them C i represents the capacitance on the i-th neuron, R i represents the resistance of the i-th neuron, x i represents the potential on the i-th neuron, tanh(x j ) is the activation function of the jth neuron, w ij is the synaptic connection strength between the i-th neuron and the j-th neuron, I i is the external stimulus current received by the i-th neuron, C i =1,R i =1,I i =0.

[0016] (4) The two-dimensional Hopfield neural network obtained from formula (iii) is:

[0017]

[0018] Where z is the potential on neuron z, u is the potential on neuron u, t is the time constant, and tanh(z) and tanh(u) are the activation functions on neurons.

[0019] (5) The two-dimensional Hindmarsh-Rose neuron and the two-dimensional Hopfield neural network are coupled through a hyperbolic tangent memristor, and a new heterogeneous neuron memristor coupling model is obtained:

[0020]

[0021] Where x and y represent the potential on the cell membrane of the two-dimensional Hindmarsh-Rose neuron and the related recovery variable respectively; z is the potential on the neuron z inside the two-dimensional Hopfield neural network; u is the potential on the neuron u inside the two-dimensional Hopfield neural network; n represents the internal magnetic flux of the coupled system; k1 is the internal parameter of the memristor, representing the coupling strength between the Hindmarsh-Rose neuron and the Hopfield neural network, and k1 is a variable.

[0022] 2. Based on system (v), a novel heterogeneous neuron memristor coupling circuit is constructed, characterized by including five circuit paths, a hyperbolic tangent analog equivalent circuit and a hyperbolic tangent memristor analog equivalent circuit:

[0023] The first circuit path module comprises a multiplier A1, a multiplier A2, a multiplier A3, a resistor R1, a resistor R2, a resistor R3, a resistor R L1 , capacitor C1, operational amplifier U1 composed of adder, inverting integrator, and resistor R 11 , resistor R 12 , and an inverter composed of an operational amplifier U2. The second stage output signal of the second circuit path is -V y The resistor R1 connected to the first circuit path; the first and second output signals V x and -V x As the input signal of the multiplier A1, the output signal of the multiplier A1 is connected to the resistor R3; the first stage output signal V x As the input signal of the multiplier A2, the output signal of the multiplier A2 is combined with the first stage output signal V x As the input signal of multiplier A3, the output signal of multiplier A3 is connected to resistor R2; the second-stage output signal of the hyperbolic tangent memristor analog equivalent circuit is -V M Connect the resistor R L1 The above resistors R1, R2, R3 and R L1 The connected signal is used as the entire input signal of the first circuit path. The output signal of the first circuit path is the first-stage output signal V x and the second stage output signal -V x .

[0024] The second circuit path module is composed of a multiplier A4, a resistor R4, a resistor R5, a resistor R S , capacitor C2, operational amplifier U3 composed of adder, inverting integrator, and resistor R 13 , resistor R 14 , and an inverter composed of an operational amplifier U4. The first stage output signal V xAs the input signal of multiplier A4, the output signal of multiplier A4 is connected to resistor R4; the positive electrode of the external DC voltage source E1 is grounded, and the negative electrode is connected to resistor R S ; The first stage output signal V of the second circuit path y Connect the resistor R5. S The connected signal is used as the entire input signal of the second circuit path. The output signal of the second circuit path is the first stage output signal V y and the second stage output signal -V y .

[0025] The third circuit path module is composed of resistors R6, R7, R8, and R L2 , capacitor C3, operational amplifier U 11 The adder, inverting integrator, and hyperbolic tangent analog equivalent circuit and the resistor R 15 , resistor R 16 、Operational amplifier U 12 The first stage output signal V of the third circuit path is z Connect resistor R8; the second-stage output signal tanh(z) of the third circuit path is connected to resistor R6; the second-stage output signal -tanh(u) of the fourth circuit path is connected to resistor R7; the first-stage output signal V of the hyperbolic tangent memristor analog equivalent circuit M Connect the resistor R L2 The above resistors R6, R7, R8 and R L2 The connected signal is used as the entire input signal of the third circuit path. The output signal of the third circuit path is the first stage output signal V z And the second stage output signal tanh(z).

[0026] The fourth circuit path module is composed of a resistor R9, a resistor R 10 , resistor R 17 , capacitor C4, operational amplifier U 13 The adder, inverting integrator and hyperbolic tangent analog equivalent circuit are composed. The first-stage output signal V u Connect the resistor R 17 The second-stage output signal tanh(z) of the third circuit path is connected to resistor R9; the second-stage output signal -tanh(u) of the fourth circuit path is connected to resistor R 10 The above resistor R9 and resistor R 10 and resistor R 17 The connected signal is used as the entire input signal of the fourth circuit path. The output signal of the fourth circuit path is the first stage output signal V u And the second stage output signal -tanh(u).

[0027] The fifth circuit path module is composed of a resistor R 18 , resistor R 19 , resistor R 20 , resistor R 21 and operational amplifier U5 to form a subtractor, resistor R 22 , resistor R 23 and the inverter composed of operational amplifier U6, resistor R 24 , capacitor C5 and operational amplifier U7 form an inverting integrator, resistor R 25 , resistor R 26 The first stage output signal V of the first circuit path is composed of an inverter composed of an operational amplifier U8 and a hyperbolic tangent analog equivalent circuit. x Connect the resistor R 18 ; The first stage output signal V of the third circuit path z Connect the resistor R 19 The above resistor R 18 and resistor R 19 The connected signal is used as the entire input signal of the fifth circuit path. The output signal of the fifth circuit path is the first-stage output signal (V x -V z ) and the second stage output signal -tanh(n).

[0028] The analog equivalent circuit of the hyperbolic tangent memristor consists of a resistor R 27 , resistor R 28 , resistor R 29 The adder composed of operational amplifier U9, multiplier A5 and resistor R 30 , resistor R 31 and operational amplifier U 10 The second stage output signal -tanh(n) of the fifth circuit path is connected to the resistor R 27 ; The positive electrode of the external DC voltage source E2 is grounded, and the negative electrode is connected to the resistor R 28 One input terminal of the multiplier A5 is connected to the output terminal of the operational amplifier U9, and the other input terminal is connected to the first stage output signal (V x -V z ). The above resistance R 27 , resistor R 28 The signal connected to the other input terminal of the multiplier A5 is used as the total input signal of the hyperbolic tangent memristor analog equivalent circuit. The total output signal of the hyperbolic tangent memristor analog equivalent circuit is the first-stage output signal V M and the second stage output signal -V M .

[0029] The hyperbolic tangent analog equivalent circuit consists of a resistor R 32 , resistor R F 、Operational amplifier U 14 , resistor R C1 , resistor R C2 , transistor T0, transistor T1, external DC current source I0, resistor R 33 , resistor R 34 , resistor R 35 , resistor R 36 、Operational amplifier U 15 Composition. Resistor R 32 One end of the equivalent circuit is connected to the input signal of the operational amplifier U 15 The output signal is the output signal of the hyperbolic tangent analog equivalent circuit.

[0030] 3. The novel heterogeneous neuron memristor coupling circuit is characterized in that: the operational amplifier U1, operational amplifier U2, operational amplifier U3, operational amplifier U4, operational amplifier U5, operational amplifier U6, operational amplifier U7, operational amplifier U8, operational amplifier U9, operational amplifier U 10 、Operational amplifier U 11 、Operational amplifier U 12 、Operational amplifier U 13 、Operational amplifier U 14 、Operational amplifier U 15 The operational amplifier models used are all TL082CP, the multiplier models used by multiplier A1, multiplier A2, multiplier A3, multiplier A4, and multiplier A5 are all AD633JN, the transistor T0 and transistor T1 are all transistor 2N2222, the value of the DC voltage source E1 is +1V, the value of the DC voltage source E2 is +0.01V, and the value of the DC current source I0 is +1.1mA.

[0031] The non-inverting input terminal of the operational amplifier U1 is grounded, and the inverting input terminal is connected to resistors R1, R2, R3, and R L1 The output end of the capacitor C1 and the input end of the capacitor C1 are connected to the output end of the resistor R 11 The input terminal and the first stage output signal V of the first circuit path x .

[0032] The non-inverting input terminal of the operational amplifier U2 is grounded, and the inverting input terminal is connected to the resistor R 11 The output terminal and resistor R 12 The input end and the output end are connected to the resistor R 12 The output terminal and the second stage output signal of the first circuit path -V x .

[0033] The non-inverting input terminal of the operational amplifier U3 is grounded, and the inverting input terminal is connected to the resistors R4, R5, and R S The output end is connected to the output end of capacitor C2 and the input end of resistor R 13 The input terminal and the first stage output signal V of the second circuit path y .

[0034] The non-inverting input terminal of the operational amplifier U4 is grounded, and the inverting input terminal is connected to the resistor R 13 The output terminal and resistor R 14 The input end and the output end are connected to the resistor R 14 The output terminal and the second circuit path of the second stage output signal -V y .

[0035] The non-inverting input terminal of the operational amplifier U5 is connected to the resistor R 19 The output terminal and resistor R 21 The inverting input terminal is connected to the resistor R 18 The output terminal and resistor R 20 The input end and the output end are connected to the resistor R 20 The output terminal and resistor R 22 The input terminal.

[0036] The non-inverting input terminal of the operational amplifier U6 is grounded, and the inverting input terminal is connected to the resistor R 22 The output terminal and resistor R 23 The input end and the output end are connected to the resistor R 23 The output terminal, resistor R 24 The input terminal and the first stage output signal (V x -V z ).

[0037] The non-inverting input terminal of the operational amplifier U7 is grounded, and the inverting input terminal is connected to the resistor R 24 The output end is connected to the output end of capacitor C5 and the input end of resistor R 25 The input terminal.

[0038] The non-inverting input terminal of the operational amplifier U8 is grounded, and the inverting input terminal is connected to the resistor R 25 The output terminal and resistor R 26 The input end and the output end are connected to the resistor R 26 The output port of the hyperbolic tangent simulation equivalent circuit and the input port of the hyperbolic tangent simulation equivalent circuit.

[0039] The non-inverting input terminal of the operational amplifier U9 is grounded, and the inverting input terminal is connected to the resistor R 27 , resistor R 28 The output terminal and resistor R29 The input end and the output end are connected to the resistor R 29 and an input of multiplier A5.

[0040] The operational amplifier U 10 The non-inverting input terminal is grounded and the inverting input terminal is connected to the resistor R 30 The output terminal and resistor R 31 The input end and the output end are connected to the resistor R 31 The output terminal and the second-stage output signal of the hyperbolic tangent memristor analog equivalent circuit -V M .

[0041] The operational amplifier U 11 The non-inverting input terminal is grounded, and the inverting input terminal is connected to resistors R6, R7, R8, and R L2 The output end of the capacitor C3 is connected to the input end of the capacitor C3, the input end of the hyperbolic tangent analog equivalent circuit and the first-stage output signal V of the third circuit path. z .

[0042] The operational amplifier U 12 The non-inverting input terminal is grounded and the inverting input terminal is connected to the resistor R 15 The output terminal and resistor R 16 The input end and the output end are connected to the resistor R 16 and the second stage output signal tanh(z) of the third circuit path.

[0043] The operational amplifier U 13 The non-inverting input terminal is grounded, and the inverting input terminal is connected to resistor R9 and resistor R 10 , resistor R 17 The output end of the capacitor C4 is connected to the input end of the capacitor C4, the input end of the hyperbolic tangent analog equivalent circuit and the first stage output signal V of the fourth circuit path. u .

[0044] The operational amplifier U 14 The non-inverting input terminal is grounded and the inverting input terminal is connected to the resistor R 32 The output terminal and resistor R F The input end and the output end are connected to the resistor R F The output end and the base of transistor T0.

[0045] The operational amplifier U 15 The non-inverting input terminal is connected to a resistor R 34 , resistor R 35 The output terminal and the inverting input terminal are connected to the resistor R 33 The output terminal and resistor R 36The input end and the output end are connected to the resistor R 36 The output end of the hyperbolic tangent simulation equivalent circuit.

[0046] One input terminal of the multiplier A1 is connected to the first stage output signal V of the first circuit path. x The other input terminal is connected to the second stage output signal -V of the first circuit path. x , the output end is connected to the input end of resistor R3.

[0047] The two input terminals of the multiplier A2 are connected to the first stage output signal V of the first circuit path. x , the output end is connected to an input end of the multiplier A3, that is, the output end of the multiplier A2 serves as an input end of the multiplier A3.

[0048] One input terminal of the multiplier A3 is connected to the first stage output signal V of the first circuit path. x , the other input end is connected to the output end of the multiplier A2, and the output end is connected to the input end of the resistor R2.

[0049] The two input terminals of the multiplier A4 are connected to the first stage output signal V of the first circuit path. x , the output end is connected to the input end of resistor R4.

[0050] One input terminal of the multiplier A5 is connected to the first stage output signal (V x -V z ), the other input end is connected to the output end of the operational amplifier U9, and the output end is connected to the resistor R 30 The input terminal and the first-stage output signal V of the hyperbolic tangent memristor analog equivalent circuit M .

[0051] The base of the transistor T0 is connected to the operational amplifier U 14 The output terminal, collector connected to the resistor R C1 The output terminal and resistor R 33 The input end of the transistor T1 has its emitter connected to the input end of the DC current source I0 and the emitter of the transistor T1.

[0052] The base of the transistor T1 is connected to a resistor R 35 The input terminal and ground, the collector is connected to the resistor R C2 The output terminal and resistor R 34 The input end of the transistor T0 is connected to the emitter of the DC current source I0 and the input end of the transistor T0.

[0053] The power supply voltages of all fifteen operational amplifiers and five multipliers are a positive voltage source of +15V and a negative voltage source of -15V; the hyperbolic tangent analog equivalent circuits appearing in the third circuit path, the fourth circuit path and the fifth circuit path are three independent circuits, that is, these are three identical circuits, not one circuit.

[0054] 4. The novel heterogeneous neuron memristive coupling circuit is characterized in that: in the first circuit path, the resistor R1=10kΩ, the resistor R2=0.1kΩ, the resistor R3=0.334kΩ, and the resistor R L1 =(1 / k1)kΩ, resistance R 11 =10kΩ, resistor R 12 =10kΩ, capacitor C1 = 10nF; in the second circuit path, resistor R4 = 0.2kΩ, resistor R5 = 10kΩ, resistor R S =10kΩ, resistor R 13 =10kΩ, resistor R 14 =10kΩ, capacitor C2 =10nF; in the third circuit path, resistor R6 =2.857kΩ, resistor R7 =100kΩ, resistor R8 =10kΩ, resistor R L2 =(1 / k1)kΩ, resistance R 15 =10kΩ, resistor R 16 =10kΩ, capacitor C3 =10nF; resistor R9 =100kΩ, resistor R 10 =16.667kΩ, resistor R 17 =10kΩ, capacitor C4 = 10nF; resistor R in the fifth circuit path 18 =10kΩ, resistor R 19 =10kΩ, resistor R 20 =10kΩ, resistor R 21 =10kΩ, resistor R 22 =10kΩ, resistor R 23 =10kΩ, resistor R 24 =10kΩ, resistor R 25 =10kΩ, resistor R 26 =10kΩ, capacitor C5 =10nF; the resistance R in the hyperbolic tangent memristor analog equivalent circuit 27 =10kΩ, resistor R 28 =10kΩ, resistor R 29 =10kΩ, resistor R 30 =10kΩ, resistor R 31 =10kΩ; the resistance R in the hyperbolic tangent simulation equivalent circuit 32 =10kΩ, resistor R F =520Ω, resistor R C1=1kΩ, resistor R C2 =1kΩ, resistor R 33 =10kΩ, resistor R 34 =10kΩ, resistor R 35 =10kΩ, resistor R 36 =10kΩ, positive voltage source VCC=+15V, negative voltage source VEE=-15V.

[0055] Beneficial effects: The present invention constructs a new heterogeneous neuron memristive coupling model by memristively coupling Hindmarsh-Rose neurons and Hopfield neural networks through memristors, and builds five circuit paths and a hyperbolic tangent memristor analog equivalent circuit and a hyperbolic tangent analog equivalent circuit through basic circuit elements to realize the circuit of the new heterogeneous neuron memristive coupling model. The circuit can generate five stable discharge modes, namely periodic spikes, chaotic spikes, random bursts, chaotic bursts, and periodic bursts. The new heterogeneous neuron memristive coupling model and circuit can not only promote the understanding of complex brain activities, but also contribute to the development of bionic systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 A schematic diagram of the circuit connection of the novel heterogeneous neuron memristor coupling model provided in an embodiment of the present invention.

[0057] Figure 2 The first-stage output signal V of the first circuit path in the circuit simulation provided by the embodiment of the present invention is x Timing diagram of the periodic spike.

[0058] Figure 3 The first-stage output signal V of the first circuit path in the circuit simulation provided by the embodiment of the present invention is x Timing diagram of the chaotic spikes.

[0059] Figure 4 The first-stage output signal V of the first circuit path in the circuit simulation provided by the embodiment of the present invention is x The timing diagram of random bursts.

[0060] Figure 5 The first-stage output signal V of the first circuit path in the circuit simulation provided by the embodiment of the present invention is x Timing diagram of chaotic bursting.

[0061] Figure 6 The first-stage output signal V of the first circuit path in the circuit simulation provided by the embodiment of the present invention is x Timing diagram of periodic bursting. DETAILED DESCRIPTION

[0062] In order to make the purpose and technical solution of the present invention more clearly understood, the application principle of the present invention is described in detail below in conjunction with the accompanying drawings and embodiments.

[0063] 1. A novel heterogeneous neuron memristor coupling model and circuit construction method, characterized by comprising the following steps:

[0064] (1) Mathematical model of the hyperbolic tangent memristor designed in the present invention:

[0065]

[0066] Where v and i represent the input voltage and output current of the memristor, t is the time constant, x is the internal magnetic flux of the memristor, k1 and c are two internal parameters of the memristor, and c = 0.01.

[0067] (2) The two-dimensional Hindmarsh-Rose neuron model is:

[0068]

[0069] Where x and y represent the potential on the neuron cell membrane and the related recovery variable respectively, I is the external stimulation current, a, b, c, d are the internal parameters related to the neuron, a=1, b=3, c=1, d=5, I=0.

[0070] (3) The mathematical model of the Hopfield neural network is:

[0071]

[0072] Among them C i represents the capacitance on the i-th neuron, R i represents the resistance of the i-th neuron, x i represents the potential on the i-th neuron, tanh(x j ) is the activation function of the jth neuron, w ij is the synaptic connection strength between the i-th neuron and the j-th neuron, I i is the external stimulus current received by the i-th neuron, C i =1,R i =1,I i =0.

[0073] (4) The two-dimensional Hopfield neural network obtained from formula (iii) is:

[0074]

[0075] Where z is the potential on neuron z, u is the potential on neuron u, t is the time constant, and tanh(z) and tanh(u) are the activation functions on neurons.

[0076] (5) The two-dimensional Hindmarsh-Rose neuron and the two-dimensional Hopfield neural network are coupled through a hyperbolic tangent memristor, and a new heterogeneous neuron memristor coupling model is obtained:

[0077]

[0078] Where x and y represent the potential on the cell membrane of the two-dimensional Hindmarsh-Rose neuron and the related recovery variable respectively; z is the potential on the neuron z inside the two-dimensional Hopfield neural network; u is the potential on the neuron u inside the two-dimensional Hopfield neural network; n represents the internal magnetic flux of the coupled system; k1 is the internal parameter of the memristor, representing the coupling strength between the Hindmarsh-Rose neuron and the Hopfield neural network, and k1 is a variable.

[0079] 2. Based on system (v), a novel heterogeneous neuron memristor coupling circuit is constructed, characterized by including five circuit paths, a hyperbolic tangent analog equivalent circuit and a hyperbolic tangent memristor analog equivalent circuit:

[0080] The first circuit path module comprises a multiplier A1, a multiplier A2, a multiplier A3, a resistor R1, a resistor R2, a resistor R3, a resistor R L1 , capacitor C1, operational amplifier U1 composed of adder, inverting integrator, and resistor R 11 , resistor R 12 , and an inverter composed of an operational amplifier U2. The second stage output signal of the second circuit path is -V y The resistor R1 connected to the first circuit path; the first and second output signals V x and -V x As the input signal of the multiplier A1, the output signal of the multiplier A1 is connected to the resistor R3; the first stage output signal V x As the input signal of the multiplier A2, the output signal of the multiplier A2 is combined with the first stage output signal V x As the input signal of multiplier A3, the output signal of multiplier A3 is connected to resistor R2; the second-stage output signal of the hyperbolic tangent memristor analog equivalent circuit is -V M Connect the resistor R L1 The above resistors R1, R2, R3 and R L1The connected signal is used as the entire input signal of the first circuit path. The output signal of the first circuit path is the first-stage output signal V x and the second stage output signal -V x .

[0081] The second circuit path module is composed of a multiplier A4, a resistor R4, a resistor R5, a resistor R S , capacitor C2, operational amplifier U3 composed of adder, inverting integrator, and resistor R 13 , resistor R 14 , and an inverter composed of an operational amplifier U4. The first stage output signal V x As the input signal of multiplier A4, the output signal of multiplier A4 is connected to resistor R4; the positive electrode of the external DC voltage source E1 is grounded, and the negative electrode is connected to resistor R S ; The first stage output signal V of the second circuit path y Connect the resistor R5. S The connected signal is used as the entire input signal of the second circuit path. The output signal of the second circuit path is the first stage output signal V y and the second stage output signal -V y .

[0082] The third circuit path module is composed of resistors R6, R7, R8, and R L2 , capacitor C3, operational amplifier U 11 The adder, inverting integrator, and hyperbolic tangent analog equivalent circuit and the resistor R 15 , resistor R 16 、Operational amplifier U 12 The first stage output signal V of the third circuit path is z Connect resistor R8; the second-stage output signal tanh(z) of the third circuit path is connected to resistor R6; the second-stage output signal -tanh(u) of the fourth circuit path is connected to resistor R7; the first-stage output signal V of the hyperbolic tangent memristor analog equivalent circuit M Connect the resistor R L2 The above resistors R6, R7, R8 and R L2 The connected signal is used as the entire input signal of the third circuit path. The output signal of the third circuit path is the first stage output signal V z And the second stage output signal tanh(z).

[0083] The fourth circuit path module is composed of a resistor R9, a resistor R 10 , resistor R 17 , capacitor C4, operational amplifier U 13The adder, inverting integrator and hyperbolic tangent analog equivalent circuit are composed. The first-stage output signal V u Connect the resistor R 17 The second-stage output signal tanh(z) of the third circuit path is connected to resistor R9; the second-stage output signal -tanh(u) of the fourth circuit path is connected to resistor R 10 The above resistor R9 and resistor R 10 and resistor R 17 The connected signal is used as the entire input signal of the fourth circuit path. The output signal of the fourth circuit path is the first stage output signal V u And the second stage output signal -tanh(u).

[0084] The fifth circuit path module is composed of a resistor R 18 , resistor R 19 , resistor R 20 , resistor R 21 and operational amplifier U5 to form a subtractor, resistor R 22 , resistor R 23 and the inverter composed of operational amplifier U6, resistor R 24 , capacitor C5 and operational amplifier U7 form an inverting integrator, resistor R 25 , resistor R 26 The first stage output signal V of the first circuit path is composed of an inverter composed of an operational amplifier U8 and a hyperbolic tangent analog equivalent circuit. x Connect the resistor R 18 ; The first stage output signal V of the third circuit path z Connect the resistor R 19 The above resistor R 18 and resistor R 19 The connected signal is used as the entire input signal of the fifth circuit path. The output signal of the fifth circuit path is the first-stage output signal (V x -V z ) and the second stage output signal -tanh(n).

[0085] The analog equivalent circuit of the hyperbolic tangent memristor consists of a resistor R 27 , resistor R 28 , resistor R 29 The adder composed of operational amplifier U9, multiplier A5 and resistor R 30 , resistor R 31 and operational amplifier U 10 The second stage output signal -tanh(n) of the fifth circuit path is connected to the resistor R 27 ; The positive electrode of the external DC voltage source E2 is grounded, and the negative electrode is connected to the resistor R 28One input terminal of the multiplier A5 is connected to the output terminal of the operational amplifier U9, and the other input terminal is connected to the first stage output signal (V x -V z ). The above resistance R 27 , resistor R 28 The signal connected to the other input terminal of the multiplier A5 is used as the total input signal of the hyperbolic tangent memristor analog equivalent circuit. The total output signal of the hyperbolic tangent memristor analog equivalent circuit is the first-stage output signal V M and the second stage output signal -V M .

[0086] The hyperbolic tangent analog equivalent circuit consists of a resistor R 32 , resistor R F 、Operational amplifier U 14 , resistor R C1 , resistor R C2 , transistor T0, transistor T1, external DC current source I0, resistor R 33 , resistor R 34 , resistor R 35 , resistor R 36 、Operational amplifier U 15 Composition. Resistor R 32 One end of the equivalent circuit is connected to the input signal of the operational amplifier U 15 The output signal is the signal of the hyperbolic tangent analog equivalent circuit.

[0087] 3. The novel heterogeneous neuron memristor coupling circuit is characterized in that: the operational amplifier U1, operational amplifier U2, operational amplifier U3, operational amplifier U4, operational amplifier U5, operational amplifier U6, operational amplifier U7, operational amplifier U8, operational amplifier U9, operational amplifier U 10 、Operational amplifier U 11 、Operational amplifier U 12 、Operational amplifier U 13 、Operational amplifier U 14 、Operational amplifier U 15 The operational amplifier models used are all TL082CP, the multiplier models used by multiplier A1, multiplier A2, multiplier A3, multiplier A4, and multiplier A5 are all AD633JN, the transistor T0 and transistor T1 are all transistor 2N2222, the value of the DC voltage source E1 is +1V, the value of the DC voltage source E2 is +0.01V, and the value of the DC current source I0 is +1.1mA.

[0088] The non-inverting input terminal of the operational amplifier U1 is grounded, and the inverting input terminal is connected to resistors R1, R2, R3, and RL1 The output end of the capacitor C1 and the input end of the capacitor C1 are connected to the output end of the resistor R 11 The input terminal and the first stage output signal V of the first circuit path x .

[0089] The non-inverting input terminal of the operational amplifier U2 is grounded, and the inverting input terminal is connected to the resistor R 11 The output terminal and resistor R 12 The input end and the output end are connected to the resistor R 12 The output terminal and the second stage output signal of the first circuit path -V x .

[0090] The non-inverting input terminal of the operational amplifier U3 is grounded, and the inverting input terminal is connected to the resistors R4, R5, and R S The output end is connected to the output end of capacitor C2 and the input end of resistor R 13 The input terminal and the first stage output signal V of the second circuit path y .

[0091] The non-inverting input terminal of the operational amplifier U4 is grounded, and the inverting input terminal is connected to the resistor R 13 The output terminal and resistor R 14 The input end and the output end are connected to the resistor R 14 The output terminal and the second circuit path of the second stage output signal -V y .

[0092] The non-inverting input terminal of the operational amplifier U5 is connected to the resistor R 19 The output terminal and resistor R 21 The inverting input terminal is connected to the resistor R 18 The output terminal and resistor R 20 The input end and the output end are connected to the resistor R 20 The output terminal and resistor R 22 The input terminal.

[0093] The non-inverting input terminal of the operational amplifier U6 is grounded, and the inverting input terminal is connected to the resistor R 22 The output terminal and resistor R 23 The input end and the output end are connected to the resistor R 23 The output terminal, resistor R 24 The input terminal and the first stage output signal (V x -V z ).

[0094] The non-inverting input terminal of the operational amplifier U7 is grounded, and the inverting input terminal is connected to the resistor R 24The output end is connected to the output end of capacitor C5 and the input end of resistor R 25 The input terminal.

[0095] The non-inverting input terminal of the operational amplifier U8 is grounded, and the inverting input terminal is connected to the resistor R 25 The output terminal and resistor R 26 The input end and the output end are connected to the resistor R 26 The output port of the hyperbolic tangent simulation equivalent circuit and the input port of the hyperbolic tangent simulation equivalent circuit.

[0096] The non-inverting input terminal of the operational amplifier U9 is grounded, and the inverting input terminal is connected to the resistor R 27 , resistor R 28 The output terminal and resistor R 29 The input end and the output end are connected to the resistor R 29 and an input of multiplier A5.

[0097] The operational amplifier U 10 The non-inverting input terminal is grounded and the inverting input terminal is connected to the resistor R 30 The output terminal and resistor R 31 The input end and the output end are connected to the resistor R 31 The output terminal and the second-stage output signal of the hyperbolic tangent memristor analog equivalent circuit -V M .

[0098] The operational amplifier U 11 The non-inverting input terminal is grounded, and the inverting input terminal is connected to resistors R6, R7, R8, and R L2 The output end of the capacitor C3 is connected to the input end of the capacitor C3, the input end of the hyperbolic tangent analog equivalent circuit and the first-stage output signal V of the third circuit path. z .

[0099] The operational amplifier U 12 The non-inverting input terminal is grounded and the inverting input terminal is connected to the resistor R 15 The output terminal and resistor R 16 The input end and the output end are connected to the resistor R 16 and the second stage output signal tanh(z) of the third circuit path.

[0100] The operational amplifier U 13 The non-inverting input terminal is grounded, and the inverting input terminal is connected to resistor R9 and resistor R 10 , resistor R 17 The output end of the capacitor C4 is connected to the input end of the capacitor C4, the input end of the hyperbolic tangent analog equivalent circuit and the first stage output signal V of the fourth circuit path. u .

[0101] The operational amplifier U 14 The non-inverting input terminal is grounded and the inverting input terminal is connected to the resistor R 32 The output terminal and resistor R F The input end and the output end are connected to the resistor R F The output end and the base of transistor T0.

[0102] The operational amplifier U 15 The non-inverting input terminal is connected to a resistor R 34 , resistor R 35 The output terminal and the inverting input terminal are connected to the resistor R 33 The output terminal and resistor R 36 The input end and the output end are connected to the resistor R 36 The output end of the hyperbolic tangent simulation equivalent circuit.

[0103] One input terminal of the multiplier A1 is connected to the first stage output signal V of the first circuit path. x The other input terminal is connected to the second stage output signal -V of the first circuit path. x , the output end is connected to the input end of resistor R3.

[0104] The two input terminals of the multiplier A2 are connected to the first stage output signal V of the first circuit path. x , the output end is connected to an input end of the multiplier A3, that is, the output end of the multiplier A2 serves as an input end of the multiplier A3.

[0105] One input terminal of the multiplier A3 is connected to the first stage output signal V of the first circuit path. x , the other input end is connected to the output end of the multiplier A2, and the output end is connected to the input end of the resistor R2.

[0106] The two input terminals of the multiplier A4 are connected to the first stage output signal V of the first circuit path. x , the output end is connected to the input end of resistor R4.

[0107] One input terminal of the multiplier A5 is connected to the first stage output signal (V x -V z ), the other input end is connected to the output end of the operational amplifier U9, and the output end is connected to the resistor R 30 The input terminal and the first-stage output signal V of the hyperbolic tangent memristor analog equivalent circuit M .

[0108] The base of the transistor T0 is connected to the operational amplifier U 14 The output terminal, collector connected to the resistor R C1The output terminal and resistor R 33 The input end of the transistor T1 has its emitter connected to the input end of the DC current source I0 and the emitter of the transistor T1.

[0109] The base of the transistor T1 is connected to a resistor R 35 The input terminal and ground, the collector is connected to the resistor R C2 The output terminal and resistor R 34 The input end of the transistor T0 is connected to the emitter of the DC current source I0 and the input end of the transistor T0.

[0110] The power supply voltages of all fifteen operational amplifiers and five multipliers are a positive voltage source of +15V and a negative voltage source of -15V; the hyperbolic tangent analog equivalent circuits appearing in the third circuit path, the fourth circuit path and the fifth circuit path are three independent circuits, that is, these are three identical circuits, not one circuit.

[0111] 4. The novel heterogeneous neuron memristive coupling circuit is characterized in that: in the first circuit path, the resistor R1=10kΩ, the resistor R2=0.1kΩ, the resistor R3=0.334kΩ, and the resistor R L1 =(1 / k1)kΩ, resistance R 11 =10kΩ, resistor R 12 =10kΩ, capacitor C1 = 10nF; in the second circuit path, resistor R4 = 0.2kΩ, resistor R5 = 10kΩ, resistor R S =10kΩ, resistor R 13 =10kΩ, resistor R 14 =10kΩ, capacitor C2 =10nF; in the third circuit path, resistor R6 =2.857kΩ, resistor R7 =100kΩ, resistor R8 =10kΩ, resistor R L2 =(1 / k1)kΩ, resistance R 15 =10kΩ, resistor R 16 =10kΩ, capacitor C3 =10nF; resistor R9 =100kΩ, resistor R 10 =16.667kΩ, resistor R 17 =10kΩ, capacitor C4 = 10nF; resistor R in the fifth circuit path 18 =10kΩ, resistor R 19 =10kΩ, resistor R 20 =10kΩ, resistor R 21 =10kΩ, resistor R 22 =10kΩ, resistor R 23 =10kΩ, resistor R 24 =10kΩ, resistor R 25 =10kΩ, resistor R 26=10kΩ, capacitor C5 =10nF; the resistance R in the hyperbolic tangent memristor analog equivalent circuit 27 =10kΩ, resistor R 28 =10kΩ, resistor R 29 =10kΩ, resistor R 30 =10kΩ, resistor R 31 =10kΩ; the resistance R in the hyperbolic tangent simulation equivalent circuit 32 =10kΩ, resistor R F =520Ω, resistor R C1 =1kΩ, resistor R C2 =1kΩ, resistor R 33 =10kΩ, resistor R 34 =10kΩ, resistor R 35 =10kΩ, resistor R 36 =10kΩ, positive voltage source VCC=+15V, negative voltage source VEE=-15V.

[0112] 5. The novel heterogeneous neuron memristor coupling circuit implemented by the circuit of the present invention is composed of five circuit paths, a hyperbolic tangent analog equivalent circuit and a hyperbolic tangent memristor analog equivalent circuit. It is verified by using Multisim simulation software. By changing the resistance R L1 , resistor R L2 The resistance value of the first circuit path and the first stage output signal V x The waveform can obtain periodic spikes such as Figure 2 As shown, the chaotic peaks are obtained as Figure 3 As shown, random clustering is obtained as Figure 4 As shown, the chaotic burst is obtained as Figure 5 As shown, the periodic burst is obtained as Figure 6 As shown in Figure 3, the feasibility and physical feasibility of the system design are verified.

Claims

1. A novel heterogeneous neuron memristor coupling model and circuit construction method, characterized in that: The following steps are involved: (1) Mathematical model of the hyperbolic tangent memristor designed in the present invention: Where v and i represent the input voltage and output current of the memristor, t is the time constant, x is the internal magnetic flux of the memristor, k1 and c are two internal parameters of the memristor, and c = 0.

01. (2) The two-dimensional Hindmarsh-Rose neuron model is: Where x and y represent the potential on the neuron cell membrane and the related recovery variable, respectively, I is the external stimulation current, a, b, c, d are internal parameters related to the neuron, a=1, b=3, c=1, d=5, I=0. (3) The mathematical model of the Hopfield neural network is: Among them C i represents the capacitance on the i-th neuron, R i represents the resistance of the ith neuron, x i represents the potential on the i-th neuron, tanh(x j ) is the activation function of the jth neuron, w ij is the synaptic connection strength between the i-th neuron and the j-th neuron, I i is the external stimulus current received by the ith neuron, C i =1,R i =1,I i =0. (4) The two-dimensional Hopfield neural network obtained from formula (iii) is: Where z is the potential on neuron z, u is the potential on neuron u, t is the time constant, and tanh(z) and tanh(u) are the activation functions on neurons. (5) The two-dimensional Hindmarsh-Rose neuron and the two-dimensional Hopfield neural network are coupled through a hyperbolic tangent memristor, and a new heterogeneous neuron memristor coupling model is obtained: Where x and y represent the potential on the cell membrane of the two-dimensional Hindmarsh-Rose neuron and the related recovery variable respectively; z is the potential on the neuron z inside the two-dimensional Hopfield neural network; u is the potential on the neuron u inside the two-dimensional Hopfield neural network; n represents the internal magnetic flux of the coupled system; k1 is the internal parameter of the memristor, representing the coupling strength between the Hindmarsh-Rose neuron and the Hopfield neural network, and k1 is a variable.

2. Based on system (v), a novel heterogeneous neuron memristor coupling circuit is constructed, characterized in that: Includes five circuit paths, a hyperbolic tangent analog equivalent circuit, and a hyperbolic tangent memristor analog equivalent circuit: The first circuit path module comprises a multiplier A1, a multiplier A2, a multiplier A3, a resistor R1, a resistor R2, a resistor R3, a resistor R L1 , capacitor C1, operational amplifier U1 composed of adder, inverting integrator, and resistor R 11 , resistor R 12 , and an inverter composed of an operational amplifier U2. The second stage output signal of the second circuit path is -V y The resistor R1 connected to the first circuit path; the first and second output signals V x and -V x As the input signal of the multiplier A1, the output signal of the multiplier A1 is connected to the resistor R3; the first stage output signal V x As the input signal of the multiplier A2, the output signal of the multiplier A2 is combined with the first stage output signal V x As the input signal of multiplier A3, the output signal of multiplier A3 is connected to resistor R2; the second-stage output signal of the hyperbolic tangent memristor analog equivalent circuit is -V M Connect the resistor R L1 The above resistors R1, R2, R3 and R L1 The connected signal is used as the entire input signal of the first circuit path. The output signal of the first circuit path is the first-stage output signal V x and the second stage output signal -V x . The second circuit path module is composed of a multiplier A4, a resistor R4, a resistor R5, a resistor R S , capacitor C2, operational amplifier U3 composed of adder, inverting integrator, and resistor R 13 , resistor R 14 , and an inverter composed of an operational amplifier U4. The first stage output signal V x As the input signal of multiplier A4, the output signal of multiplier A4 is connected to resistor R4; the positive electrode of the external DC voltage source E1 is grounded, and the negative electrode is connected to resistor R S ; The first stage output signal V of the second circuit path y Connect the resistor R5. S The connected signal is used as the entire input signal of the second circuit path. The output signal of the second circuit path is the first stage output signal V y and the second stage output signal -V y . The third circuit path module is composed of resistors R6, R7, R8, and R L2 , capacitor C3, operational amplifier U 11 The adder, inverting integrator, and hyperbolic tangent analog equivalent circuit and the resistor R 15 , resistor R 16 、Operational amplifier U 12 The first stage output signal V of the third circuit path is z Connect resistor R8; the second-stage output signal tanh(z) of the third circuit path is connected to resistor R6; the second-stage output signal -tanh(u) of the fourth circuit path is connected to resistor R7; the first-stage output signal V of the hyperbolic tangent memristor analog equivalent circuit M Connect the resistor R L2 The above resistors R6, R7, R8 and R L2 The connected signal is used as the entire input signal of the third circuit path. The output signal of the third circuit path is the first stage output signal V z And the second stage output signal tanh(z). The fourth circuit path module is composed of a resistor R9, a resistor R 10 , resistor R 17 , capacitor C4, operational amplifier U 13 The adder, inverting integrator and hyperbolic tangent analog equivalent circuit are composed. The first-stage output signal V u Connect the resistor R 17 The second-stage output signal tanh(z) of the third circuit path is connected to resistor R9; the second-stage output signal -tanh(u) of the fourth circuit path is connected to resistor R 10 The above resistor R9 and resistor R 10 and resistor R 17 The connected signal is used as the entire input signal of the fourth circuit path. The output signal of the fourth circuit path is the first stage output signal V u And the second stage output signal -tanh(u). The fifth circuit path module is composed of a resistor R 18 , resistor R 19 , resistor R 20 , resistor R 21 and operational amplifier U5 to form a subtractor, resistor R 22 , resistor R 23 and the inverter composed of operational amplifier U6, resistor R 24 , capacitor C5 and operational amplifier U7 form an inverting integrator, resistor R 25 , resistor R 26 The first stage output signal V of the first circuit path is composed of an inverter composed of an operational amplifier U8 and a hyperbolic tangent analog equivalent circuit. x Connect the resistor R 18 ; The first stage output signal V of the third circuit path z Connect the resistor R 19 The above resistor R 18 and resistor R 19 The connected signal is used as the entire input signal of the fifth circuit path. The output signal of the fifth circuit path is the first-stage output signal (V x -V z ) and the second stage output signal -tanh(n). The analog equivalent circuit of the hyperbolic tangent memristor consists of a resistor R 27 , resistor R 28 , resistor R 29 The adder composed of operational amplifier U9, multiplier A5 and resistor R 30 , resistor R 31 and operational amplifier U 10 The second stage output signal -tanh(n) of the fifth circuit path is connected to the resistor R 27 ; The positive electrode of the external DC voltage source E2 is grounded, and the negative electrode is connected to the resistor R 28 One input terminal of the multiplier A5 is connected to the output terminal of the operational amplifier U9, and the other input terminal is connected to the first stage output signal (V x -V z ). The above resistance R 27 , resistor R 28 The signal connected to the other input terminal of the multiplier A5 is used as the total input signal of the hyperbolic tangent memristor analog equivalent circuit. The total output signal of the hyperbolic tangent memristor analog equivalent circuit is the first-stage output signal V M and the second stage output signal -V M . The hyperbolic tangent analog equivalent circuit consists of a resistor R 32 , resistor R F 、Operational amplifier U 14 , resistor R C1 , resistor R C2 , transistor T0, transistor T1, external DC current source I0, resistor R 33 , resistor R 34 , resistor R 35 , resistor R 36 、Operational amplifier U 15 Composition. Resistor R 32 One end of the equivalent circuit is connected to the input signal of the operational amplifier U 15 The output signal is the signal of the hyperbolic tangent analog equivalent circuit.

3. A novel heterogeneous neuron memristor coupling circuit according to claim 2, characterized in that: The operational amplifier U1, operational amplifier U2, operational amplifier U3, operational amplifier U4, operational amplifier U5, operational amplifier U6, operational amplifier U7, operational amplifier U8, operational amplifier U9, operational amplifier U 10 、Operational amplifier U 11 、Operational amplifier U 12 、Operational amplifier U 13 、Operational amplifier U 14 、Operational amplifier U 15 The operational amplifier models used are all TL082CP, the multiplier models used by multiplier A1, multiplier A2, multiplier A3, multiplier A4, and multiplier A5 are all AD633JN, the transistor T0 and transistor T1 are all transistor 2N2222, the value of the DC voltage source E1 is +1V, the value of the DC voltage source E2 is +0.01V, and the value of the DC current source I0 is +1.1mA.

4. The novel heterogeneous neuron memristor coupling circuit according to claim 2, characterized in that: In the first circuit path, the resistor R1=10kΩ, the resistor R2=0.1kΩ, the resistor R3=0.334kΩ, and the resistor R L1 =(1 / k1)kΩ, resistance R 11 =10kΩ, resistor R 12 =10kΩ, capacitor C1 = 10nF; In the second circuit path, resistor R4 = 0.2 kΩ, resistor R5 = 10 kΩ, and resistor R S =10kΩ, resistor R 13 =10kΩ, resistor R 14 =10kΩ, capacitor C2 =10nF; in the third circuit path, resistor R6 =2.857kΩ, resistor R7 =100kΩ, resistor R8 =10kΩ, resistor R L2 =(1 / k1)kΩ, resistance R 15 =10kΩ, resistor R 16 =10kΩ, capacitor C3 =10nF; resistor R9 =100kΩ, resistor R 10 =16.667kΩ, resistor R 17 =10kΩ, capacitor C4 = 10nF; The resistance R in the fifth circuit path 18 =10kΩ, resistor R 19 =10kΩ, resistor R 20 =10kΩ, resistor R 21 =10kΩ, resistor R 22 =10kΩ, resistor R 23 =10kΩ, resistor R 24 =10kΩ, resistor R 25 =10kΩ, resistor R 26 =10kΩ, capacitor C5 =10nF; the resistance R in the hyperbolic tangent memristor analog equivalent circuit 27 =10kΩ, resistor R 28 =10kΩ, resistor R 29 =10kΩ, resistor R 30 =10kΩ, resistor R 31 =10kΩ; the resistance R in the hyperbolic tangent simulation equivalent circuit 32 =10kΩ, resistor R F =520Ω, resistor R C1 =1kΩ, resistor R C2 =1kΩ, resistor R 33 =10kΩ, resistor R 34 =10kΩ, resistor R 35 =10kΩ, resistor R 36 =10kΩ, positive voltage source VCC=+15V, negative voltage source VEE=-15V.

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