A small-scale hopfield neural network circuit based on memristors

Abstract

The application discloses a small-scale Hopfield neural network circuit based on a memristor, which comprises an activation function module circuit, a memristor model circuit and a Hopfield neural network circuit; the Hopfield neural network circuit comprises three neuron networks X1, X2 and X3; and a connection weight in the Hopfeild neural network is replaced by the memristor module circuit to obtain a new neural network. By replacing the synaptic weight of the Hopfield neural network system, it is found that the originally stable system exhibits rich dynamic behaviors, including chaos, hyperchaos, quasi-periodicity, double-vortex attractor and the like. The circuit is simple in design, and can adjust the weight parameters Rr and the parameter w32 to realize various dynamic behaviors. Therefore, the circuit can be used in the field of secret communication and is helpful for the research on the nervous system.

Description

Technical Field

[0001] This invention relates to the field of Hopfield neural network circuit technology, and in particular to a small-scale Hopfield neural network circuit based on memristors. Background Technology

[0002] Hopfield neural networks are recurrent neural networks with a network structure similar to real biological neural networks, capable of generating complex and rich dynamic behaviors. Memristors, possessing transmission and memory functions, hold significant application potential in chaotic circuits, secure communication, and neural networks. Memristors can simulate the synaptic function of neurons, and memristor-based Hopfield neural networks have become a research hotspot.

[0003] CN110097182A discloses a circuit for implementing a three-dimensional Hopfield neural network model controlled by a neural activation gradient λ. Based on a conventional three-dimensional Hopfield neural network, a neural activation gradient is introduced into the hyperbolic tangent function as the control quantity λ of the model, forming an activation function tanh(λx) based on the neural activation gradient. The activation function serves as a module of the neural network, and the dynamic control of the three-dimensional Hopfield neural network can be achieved through the neural activation gradient λ. This control method is simple and easy to operate, and it simulates the reaction state of the human brain very well. It has good applications for the development and research of neuromorphic circuits, electronic neurons, and artificial intelligence. Summary of the Invention

[0004] The circuit implementation of the three-dimensional Hopfield neural network model controlled by neural activation gradient λ disclosed in CN110097182A has a finite number of isolated equilibrium points, which is consistent with most Hopfield neural networks. This invention solves this problem by proposing a Hopfield neural network with a single equilibrium point. It exhibits stronger noise resistance in associative memory tasks, effectively avoids the problem of traditional Hopfield networks easily getting trapped in local optima, and is adaptable to a wider range of scenarios.

[0005] Therefore, this invention presents a small-scale Hopfield neural network circuit based on memristors. This circuit replaces one connection weight in the Hopfield neural network with a memristor model circuit to obtain a new neural network. By replacing the synaptic weights, it was found that the originally stable system exhibits rich dynamic behaviors, including chaotic, hyperchaotic, quasi-periodic, and double-vortex attractor phenomena. The circuit design of this invention is simple, and various dynamic behaviors can be achieved by adjusting the weight parameters Rr and w32. Therefore, it can be used in the field of secure communication and contributes to the research of nervous systems.

[0006] Therefore, the technical solution adopted in this invention is: a small-scale Hopfield neural network circuit based on memristor, comprising three neuron networks X1, X2, and X3, the circuit equation of the i-th neuron is shown below:

[0007] (1)

[0008] in Indicates the first The state variable of the voltage across a capacitor. This represents the membrane resistance between the inside and outside of a neuron. This represents the input bias current, corresponding to the threshold of the neuron. This represents the activation function, which is usually an sigmoid function with an upper and a lower bound. It means The weight matrix is ​​called the synaptic weight matrix. Indicates the first The first neuron and the second The connection strength between neurons corresponds to the admittance between neurons. The activation function and the... The first neuron and the second Connection strength between neurons The product of these two terms represents the electrical current between neurons. The activation function is chosen as follows: . This represents the input to the j-th neuron.

[0009] and memory All have units of admittance, so use replace , , , , Activation functions are used to characterize the two states of a neuron: excitation or inhibition. It is the magnetic flux variable of the memristor The current variable at the memristor port is a key dynamic quantity connecting the neuron state with the electrical characteristics of the memristor.

[0010] Pick , , absolute value Indicates the strength of the memristor;

[0011] because We have ,So Therefore, the remaining three equations are independent of , Right now It can take any real constant, which means that the equilibrium points of the system must be composed of a single line.

[0012] The system equations for a small-scale Hopfield neural network based on memristors are shown below:

[0013] (2)

[0014] in:

[0015] , , .

[0016] Specifically, a small-scale Hopfield neural network circuit based on memristors includes an activation function module circuit, a memristor model circuit, and a Hopfield neural network circuit; the Hopfield neural network circuit includes three neuron networks X1, X2, and X3, with one connection weight in the Hopfield neural network replaced by the memristor module circuit.

[0017] Furthermore, the memristor module circuit includes a resistor R, a capacitor C, an operational amplifier, and multipliers D2 and D3; input V1 is connected to one end of resistor R, the other end of R is connected to the inverting input of the operational amplifier, and the non-inverting input of the operational amplifier is grounded; the two ends of capacitor C are connected to the inverting input and output of the operational amplifier, respectively; the output of the operational amplifier is connected to the two inputs of multiplier D2; the output of multiplier D2 and input V1 are connected to the two inputs of multiplier D3, and output V2.

[0018] Resistance value ,capacitance The multipliers D2 and D3 are model AD633.

[0019] Furthermore, the activation function module circuit includes a resistor R. t1 Resistance R t2 Resistance R t3 Resistance R t4 Resistance R t5 Resistance R t6 Resistance R t7 Resistance R t8 Resistance R t9 Resistance R t10 Operational amplifiers U1 and U2; transistors Q1, Q2, Q3, and Q4; DC voltage sources VCC and VEE; resistor R. t1 One end is connected to the input terminal vi, and the resistor R t1 The other end is connected to the inverting input of operational amplifier U1, and a resistor R is connected in parallel between the inverting input and output of operational amplifier U1. t2The positive input terminal of operational amplifier U1 is grounded, and the output terminal of operational amplifier U1 is connected to the base of NPN transistor Q1. The collector of transistor Q1 is connected to resistor R. t3 One end is connected, resistor R t3 The other end is connected to a DC voltage source VCC; the DC voltage source VCC and resistor R t4 One end is connected, resistor R t4 The other end is connected to the collector of NPN transistor Q2. The emitter of transistor Q2 is the common output terminal of the emitter of transistor Q1 and is connected to the collector of transistor Q3. The emitter of transistor Q3 is connected to resistor R. t9 One end, R t9 The other end is connected to a resistor R. t10 One end is connected in parallel to a DC voltage source VDD; R t10 The other end is connected to the emitter of transistor Q4; the bases of transistors Q3 and Q4 are connected; the collector of transistor Q4 is connected to the base of transistor Q4 and then connected to the variable resistor R. X1 At one end, the sliding rheostat R X1 The other end is grounded; the collector of transistor Q1 is simultaneously connected to resistor R. t5 One end is connected, resistor R t5 The other end is connected to the inverting input of operational amplifier U2; a resistor R is connected in parallel between the inverting input and output of operational amplifier U2. t6 The base of transistor Q2 and resistor R t8 One end is connected to ground, and the resistance is R. t8 The other end is connected to the non-inverting input of operational amplifier U2; the non-inverting input of U2 is also connected to resistor R. t7 One end, R t7 The other end is connected to the collector of transistor Q2, and the output voltage of U2 is -tanh(vi).

[0020] Resistance value The DC power supply voltage is 5V.

[0021] Furthermore, the neuron X1 includes: resistors R1, R2, R3, and R... 11 resistance R 12 resistance R 13 Capacitor C1, operational amplifiers A1 and A2, activation function module circuit; input x connected to one end of resistor R1, input -va connected to resistor R 11 One end, the input VB is connected to resistor R. 12 One end, the input VC is connected to resistor R. 13 One end; resistor R1, resistor R 11 resistance R 12 and resistance R 13The other end is connected to the inverting input of operational amplifier A1; the two ends of capacitor C1 are connected to the inverting input and output of operational amplifier A1 respectively, and output the x signal; the output of operational amplifier A1 is connected to the activation function module circuit to output va and connected to one end of resistor R2; the other end of resistor R2 is connected to the inverting input of operational amplifier A2; the two ends of resistor R3 are connected to the inverting input and output of operational amplifier A2 respectively, and output the -va signal; the non-inverting inputs of operational amplifiers A1 and A2 are grounded.

[0022] The neuron X2 includes: resistors R4, R5, R6, and R... 21 resistance R 22 Capacitor C2, operational amplifiers A3 and A4, activation function module circuit and memristor model circuit; input y is connected to one end of resistor R4, input -va is connected to one end of memristor model circuit; the other end of memristor model circuit is connected to resistor R. 21 One end, the input VB is connected to resistor R. 22 One end; resistor R4, resistor R 21 and resistance R 22 The other end is connected to the inverting input of operational amplifier A3; the two ends of capacitor C2 are connected to the inverting input and output of operational amplifier A3 respectively, and output a y signal; the output of operational amplifier A3 is connected to the activation function module circuit to output vb and connected to one end of resistor R5; the other end of resistor R5 is connected to the inverting input of operational amplifier A4; the two ends of resistor R6 are connected to the inverting input and output of operational amplifier A4 respectively, and output a -vb signal; the non-inverting inputs of operational amplifiers A3 and A4 are grounded.

[0023] The neuron X3 includes: resistors R7, R8, R9, and R... 31 resistance R 32 resistance R 33 Capacitor C3, operational amplifiers A5 and A6, activation function module circuit; input z is connected to one end of resistor R7, input va is connected to resistor R 31 One end, the input -vb is connected to resistor R. 32 One end, the input VC is connected to resistor R. 33 One end; resistor R7, resistor R 31 resistance R 32 and resistance R 33 The other end is connected to the inverting input of operational amplifier A5; the two ends of capacitor C3 are connected to the inverting input and output of operational amplifier A5 respectively, and output the z signal; the output of operational amplifier A5 is connected to the activation function module circuit output vc and connected to resistor R8; the other end of resistor R8 is connected to the inverting input of operational amplifier A6; the two ends of resistor R9 are connected to the inverting input and output of operational amplifier A6 respectively, and output the signal -vc; the non-inverting inputs of operational amplifiers A5 and A6 are grounded.

[0024] The resistance and capacitance values ​​are as follows:

[0025] ;

[0026] ;

[0027] , where Rr is an adjustable resistor;

[0028] ;

[0029] .

[0030] because We have ,So Therefore, the remaining three equations are independent of , Right now The constant can be any real value, allowing the Hopfield neural network of this invention to have a linear equilibrium point. It exhibits stronger noise resistance in associative memory tasks, effectively avoiding the problem of traditional Hopfield networks easily getting trapped in local optima, and is adaptable to a wider range of scenarios. Attached Figure Description

[0031] Figure 1 It is a neural network connection graph;

[0032] Figure 2 This is the implementation circuit of the neural network of this invention;

[0033] Figure 3 It is a memristor model circuit;

[0034] Figure 4 It is the activation function - tanh module circuit;

[0035] Figure 5 It is a three-dimensional phase diagram of a neural network;

[0036] Figure 6 It is a two-dimensional phase diagram of a neural network;

[0037] Figure 7 It is a time-domain waveform diagram of a neural network;

[0038] Figure 8 It is a neural network LE diagram;

[0039] Figure 9 It is a neural network bifurcation diagram;

[0040] Figure 10 It is the phase diagram of the neural network system as r changes;

[0041] Figure 11 It is an asymmetric coexistence attractor for neural networks;

[0042] Figure 12It is a neural network double-vortex attractor;

[0043] Figure 13 It is a chaotic attractor for neural network circuits;

[0044] Figure 14 It is a double-vortex attractor for neural network circuits. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0046] A small-scale Hopfield neural network circuit based on memristor, comprising three neuron networks X1, X2, and X3, such as Figure 1 As shown.

[0047] The circuit equation for the i-th neuron is shown below:

[0048] (1)

[0049] in Indicates the first The state variable of the voltage across a capacitor. This represents the membrane resistance between the inside and outside of a neuron. This represents the input bias current, corresponding to the threshold of the neuron. This represents the activation function, which is usually an sigmoid function with an upper and a lower bound. It means The weight matrix is ​​called the synaptic weight matrix. Indicates the first The first neuron and the second The connection strength between neurons corresponds to the admittance between neurons. The activation function and the... The first neuron and the second Connection strength between neurons The product of these two terms represents the electrical current between neurons. The activation function is chosen as follows: .

[0050] This represents the input to the j-th neuron.

[0051] and memory All have units of admittance, so use replace , , , , Activation functions are used to characterize the two states of a neuron: excitation or inhibition. It is the magnetic flux variable of the memristor The current variable at the memristor port is a key dynamic quantity connecting the neuron state with the electrical characteristics of the memristor.

[0052] Set RC=1, =10kΩ, =100nF.

[0053] Pick , , here It's a new parameter. Its absolute value... This indicates the strength of the memristor. Therefore, the system equations for a small-scale Hopfield neural network based on memristor are as follows:

[0054] (2)

[0055] in:

[0056] , , .

[0057] like Figure 2 As shown, a small-scale Hopfield neural network circuit based on memristors includes an activation function module circuit, a memristor model circuit, and a Hopfield neural network circuit. The Hopfield neural network circuit includes three neuron networks X1, X2, and X3. A new neural network is obtained by replacing one connection weight in the Hopfield neural network with the memristor module circuit.

[0058] The neuron X1 includes: resistors R1, R2, R3, and R... 11 resistance R 12 resistance R 13 The circuit consists of capacitor C1, operational amplifiers A1 and A2, and the activation function module. Input x is connected to one end of resistor R1, and input -va is connected to resistor R. 11 One end, the input VB is connected to resistor R. 12 One end, the input VC is connected to resistor R. 13 One end; resistor R1, resistor R 11 resistance R 12 and resistance R 13The other end is connected to the inverting input of operational amplifier A1; the two ends of capacitor C1 are connected to the inverting input and output of operational amplifier A1 respectively, and output the x signal; the output of operational amplifier A1 is connected to the activation function module circuit to output va and connected to one end of resistor R2; the other end of resistor R2 is connected to the inverting input of operational amplifier A2; the two ends of resistor R3 are connected to the inverting input and output of operational amplifier A2 respectively, and output the -va signal; the non-inverting inputs of operational amplifiers A1 and A2 are grounded.

[0059] The neuron X2 includes: resistors R4, R5, R6, and R... 21 resistance R 22 The circuit consists of capacitor C2, operational amplifiers A3 and A4, an activation function module circuit, and a memristor model circuit. Input y is connected to one end of resistor R4, and input -va is connected to one end of the memristor model circuit; the other end of the memristor model circuit is connected to resistor R. 21 One end, the input VB is connected to resistor R. 22 One end; resistor R4, resistor R 21 and resistance R 22 The other end is connected to the inverting input of operational amplifier A3; the two ends of capacitor C2 are connected to the inverting input and output of operational amplifier A3 respectively, and output a y signal; the output of operational amplifier A3 is connected to the activation function module circuit to output vb and connected to one end of resistor R5; the other end of resistor R5 is connected to the inverting input of operational amplifier A4; the two ends of resistor R6 are connected to the inverting input and output of operational amplifier A4 respectively, and output a -vb signal; the non-inverting inputs of operational amplifiers A3 and A4 are grounded.

[0060] The neuron X3 includes: resistors R7, R8, R9, and R... 31 resistance R 32 resistance R 33 The circuit consists of capacitor C3, operational amplifiers A5 and A6, and the activation function module. Input z is connected to one end of resistor R7, and input va is connected to resistor R. 31 One end, the input -vb is connected to resistor R. 32 One end, the input VC is connected to resistor R. 33 One end; resistor R7, resistor R 31 resistance R 32 and resistance R 33 The other end is connected to the inverting input of operational amplifier A5; the two ends of capacitor C3 are connected to the inverting input and output of operational amplifier A5 respectively, and output the z signal; the output of operational amplifier A5 is connected to the activation function module circuit output vc and connected to resistor R8; the other end of resistor R8 is connected to the inverting input of operational amplifier A6; the two ends of resistor R9 are connected to the inverting input and output of operational amplifier A6 respectively, and output the signal -vc; the non-inverting inputs of operational amplifiers A5 and A6 are grounded.

[0061] The resistance and capacitance values ​​in this embodiment are as follows:

[0062] ;

[0063] ;

[0064] , where Rr is an adjustable resistor;

[0065]

[0066]

[0067] like Figure 3 As shown, the memristor model circuit includes a resistor R, a capacitor C, an operational amplifier, and multipliers D2 and D3. Input V1 is connected to one end of resistor R, and the other end of R is connected to the inverting input of the operational amplifier. The non-inverting input of the operational amplifier is grounded. The two ends of capacitor C are connected to the inverting input and output of the operational amplifier, respectively. The output of the operational amplifier is connected to the two inputs of multiplier D2. The output of multiplier D2 and input V1 are connected to the two inputs of multiplier D3, and the output is V2.

[0068] The resistance value is The multipliers D2 and D3 are model AD633.

[0069] like Figure 4 As shown, the activation function module circuit includes resistor R. t1 Resistance R t2 Resistance R t3 Resistance R t4 Resistance R t5 Resistance R t6 Resistance R t7 Resistance R t8 Resistance R t9 Resistance R t10 Operational amplifiers U1 and U2; transistors Q1, Q2, Q3, and Q4; DC voltage sources VCC and VEE; resistor R. t1 One end is connected to the input terminal vi, and the resistor R t1 The other end is connected to the inverting input of operational amplifier U1, and a resistor R is connected in parallel between the inverting input and output of operational amplifier U1. t2 The positive input terminal of operational amplifier U1 is grounded, and the output terminal of operational amplifier U1 is connected to the base of NPN transistor Q1. The collector of transistor Q1 is connected to resistor R. t3 One end is connected, resistor R t3 The other end is connected to a DC voltage source VCC; the DC voltage source VCC and resistor R t4 One end is connected, resistor R t4The other end is connected to the collector of NPN transistor Q2. The emitter of transistor Q2 is the common output terminal of the emitter of transistor Q1 and is connected to the collector of transistor Q3. The emitter of transistor Q3 is connected to resistor R. t9 One end, R t9 The other end is connected to a resistor R. t10 One end is connected in parallel to a DC voltage source VDD; R t10 The other end is connected to the emitter of transistor Q4; the bases of transistors Q3 and Q4 are connected; the collector of transistor Q4 is connected to the base of transistor Q4 and then connected to the variable resistor R. X1 At one end, the sliding rheostat R X1 The other end is grounded. The collector of transistor Q1 is simultaneously connected to resistor R. t5 One end is connected, resistor R t5 The other end is connected to the inverting input of operational amplifier U2; a resistor R is connected in parallel between the inverting input and output of operational amplifier U2. t6 The base of transistor Q2 and resistor R t8 One end is connected to ground, and the resistance is R. t8 The other end is connected to the non-inverting input of operational amplifier U2; the non-inverting input of U2 is also connected to resistor R. t7 One end, R t7 The other end is connected to the collector of transistor Q2, and the output voltage of U2 is -tanh(vi).

[0070] In the above activation function module circuit: the resistance value is The DC power supply voltage is 5V.

[0071] A bifurcation graph of a small-scale Hopfield neural network based on memristor is shown below. Figure 8 And the Lyapunov index spectrum, as shown Figure 9 And the system phase diagram that varies with memristor strength r ( Figure 5 , Figure 6 , Figure 11 , Figure 12 It can be observed that when a memristor is added as a neuron synaptic weight in a Hopfield neural network system, the system exhibits rich dynamic behaviors: chaos, hyperchaos, quasi-periodicity, and asymmetric coexistence attractors. The quasi-periodic state, hyperchaotic state, and chaotic state of the system are plotted by adjusting the strength of the memristor. Figure 13 , Figure 14 The system phase diagrams observed using an oscilloscope in the MULTISIM simulation software verified the numerical simulation results. Notably, when the parameter w32 = -3 was modified, the system's attractor changed from a single-vortex to a double-vortex, making its topology more complex, as shown below. Figure 12-14 .

Claims

1. A small-scale Hopfield neural network circuit based on memristors, characterized in that: The circuit equation for the i-th neuron, consisting of three neural networks X1, X2, and X3, is shown below: （1） in Indicates the first The state variable of the voltage across a capacitor. This represents the membrane resistance between the inside and outside of a neuron. This represents the input bias current, corresponding to the threshold of the neuron; This represents the activation function. express The weight matrix is ​​called the synaptic weight matrix. Indicates the first The first neuron and the second The connection strength between the first neuron corresponds to the admittance between neurons, and the activation function is related to the first neuron. The first neuron and the second Connection strength between neurons The product of these is represented as the current between neurons, and the activation function is chosen as: ; This represents the input to the j-th neuron; and memory All have units of admittance, so use replace , , , , Activation functions are used to characterize the two states of a neuron: excitation or inhibition. It is the flux variable of the memristor. The current variable at the memristor port is a key dynamic quantity connecting the neuron state with the electrical characteristics of the memristor. Pick , , absolute value Indicates the strength of the memristor; The system equations for a small-scale Hopfield neural network based on memristors are shown below: （2） in: ， ， 。 2. The small-scale Hopfield neural network circuit based on memristor according to claim 1, characterized in that: It includes an activation function module circuit, a memristor model circuit, and a Hopfield neural network circuit; the Hopfield neural network circuit includes three neuron networks X1, X2, and X3, with a memristor module circuit replacing one of the connection weights in the Hopfield neural network.

3. The small-scale Hopfield neural network circuit based on memristors according to claim 2, characterized in that: The memristor module circuit includes a resistor R, a capacitor C, an operational amplifier, and multipliers D2 and D3. Input V1 is connected to one end of resistor R, and the other end of R is connected to the inverting input of the operational amplifier. The non-inverting input of the operational amplifier is grounded. The two ends of capacitor C are connected to the inverting input and output of the operational amplifier, respectively. The output of the operational amplifier is connected to the two inputs of multiplier D2. The output of multiplier D2 and input V1 are connected to the two inputs of multiplier D3, and output V2 is generated.

4. The small-scale Hopfield neural network circuit based on memristor according to claim 3, characterized in that: Resistance value ,capacitance The multipliers D2 and D3 are model AD633.

5. The small-scale Hopfield neural network circuit based on memristor according to claim 2, characterized in that: The activation function module circuit includes a resistor R. t1 Resistance R t2 Resistance R t3 Resistance R t4 Resistance R t5 Resistance R t6 Resistance R t7 Resistance R t8 Resistance R t9 Resistance R t10 Operational amplifiers U1 and U2; transistors Q1, Q2, Q3, and Q4; DC voltage sources VCC and VEE; resistor R. t1 One end is connected to the input terminal vi, and the resistor R t1 The other end is connected to the inverting input of operational amplifier U1, and a resistor R is connected in parallel between the inverting input and output of operational amplifier U1. t2 The positive input terminal of operational amplifier U1 is grounded, and the output terminal of operational amplifier U1 is connected to the base of NPN transistor Q1. The collector of transistor Q1 is connected to resistor R. t3 One end is connected, resistor R t3 The other end is connected to a DC voltage source VCC; the DC voltage source VCC and resistor R t4 One end is connected, resistor R t4 The other end is connected to the collector of NPN transistor Q2. The emitter of transistor Q2 is the common output terminal of the emitter of transistor Q1 and is connected to the collector of transistor Q3. The emitter of transistor Q3 is connected to resistor R. t9 One end, R t9 The other end is connected to a resistor R. t10 One end is connected in parallel to a DC voltage source VDD; R t10 The other end is connected to the emitter of transistor Q4; the bases of transistors Q3 and Q4 are connected; the collector of transistor Q4 is connected to the base of transistor Q4 and then connected to the variable resistor R. X1 At one end, the sliding rheostat R X1 The other end is grounded; the collector of transistor Q1 is simultaneously connected to resistor R. t5 One end is connected, resistor R t5 The other end is connected to the inverting input of operational amplifier U2; a resistor R is connected in parallel between the inverting input and output of operational amplifier U2. t6 The base of transistor Q2 and resistor R t8 One end is connected to ground, and the resistance is R. t8 The other end is connected to the non-inverting input of operational amplifier U2; the non-inverting input of U2 is also connected to resistor R. t7 One end, R t7 The other end is connected to the collector of transistor Q2, and the output voltage of U2 is -tanh(vi).

6. The small-scale Hopfield neural network circuit based on memristor according to claim 5, characterized in that: Resistance value The DC power supply voltage is 5V.

7. The small-scale Hopfield neural network circuit based on memristor according to claim 2, characterized in that: The neuron X1 includes: resistor R1, resistor R2, resistor R3, and resistor R... 11 resistance R 12 resistance R 13 Capacitor C1, operational amplifiers A1 and A2, activation function module circuit; input x connected to one end of resistor R1, input -va connected to resistor R 11 One end, the input VB is connected to resistor R. 12 One end, the input VC is connected to resistor R. 13 One end; resistor R1, resistor R 11 resistance R 12 and resistance R 13 The other end is connected to the inverting input of operational amplifier A1; the two ends of capacitor C1 are connected to the inverting input and output of operational amplifier A1 respectively, and output the x signal; the output of operational amplifier A1 is connected to the activation function module circuit to output va and connected to one end of resistor R2; the other end of resistor R2 is connected to the inverting input of operational amplifier A2; the two ends of resistor R3 are connected to the inverting input and output of operational amplifier A2 respectively, and output the -va signal; the non-inverting inputs of operational amplifiers A1 and A2 are grounded.

8. The small-scale Hopfield neural network circuit based on memristor according to claim 2, characterized in that: The neuron X2 includes: resistors R4, R5, R6, and R... 21 resistance R 22 Capacitor C2, operational amplifiers A3 and A4, activation function module circuit and memristor model circuit; input y is connected to one end of resistor R4, input -va is connected to one end of memristor model circuit; the other end of memristor model circuit is connected to resistor R. 21 One end, the input VB is connected to resistor R. 22 One end; resistor R4, resistor R 21 and resistance R 22 The other end is connected to the inverting input of operational amplifier A3; the two ends of capacitor C2 are connected to the inverting input and output of operational amplifier A3 respectively, and output a y signal; the output of operational amplifier A3 is connected to the activation function module circuit to output vb and connected to one end of resistor R5; the other end of resistor R5 is connected to the inverting input of operational amplifier A4; the two ends of resistor R6 are connected to the inverting input and output of operational amplifier A4 respectively, and output a -vb signal; the non-inverting inputs of operational amplifiers A3 and A4 are grounded.

9. The small-scale Hopfield neural network circuit based on memristor according to claim 2, characterized in that: The neuron X3 includes: resistors R7, R8, R9, and R... 31 resistance R 32 resistance R 33 Capacitor C3, operational amplifiers A5 and A6, activation function module circuit; input z is connected to one end of resistor R7, input va is connected to resistor R 31 One end, the input -vb is connected to resistor R. 32 One end, the input VC is connected to resistor R. 33 One end; resistor R7, resistor R 31 resistance R 32 and resistance R 33 The other end is connected to the inverting input of operational amplifier A5; the two ends of capacitor C3 are connected to the inverting input and output of operational amplifier A5 respectively, and output the z signal; the output of operational amplifier A5 is connected to the activation function module circuit output vc and connected to resistor R8; the other end of resistor R8 is connected to the inverting input of operational amplifier A6; the two ends of resistor R9 are connected to the inverting input and output of operational amplifier A6 respectively, and output the signal -vc; the non-inverting inputs of operational amplifiers A5 and A6 are grounded.

10. A small-scale Hopfield neural network circuit based on memristor according to claim 7, 8, or 9, characterized in that: The resistance and capacitance values ​​are as follows: ； ； , where Rr is an adjustable resistor; ； 。

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