Memristive coupling neuron circuit based on N-type local active memristor

Abstract

The invention discloses a memristive coupling neuron circuit based on an N-type local active memristor. The memristive coupling neuron circuit is composed of a first memristive neuron module, a second memristive neuron module and a synaptic module. The N-type local active memristor is an overall passive but local active memristor, and shows an N-type negative differential conductivity characteristic in a DC V-I curve. Two memristive neuron modules are coupled through an N-type local active memristor to form a memristive coupling neuron circuit, and two neurons reproduce the Smale paradox phenomenon and the conversion from oscillation to chaos by adjusting appropriate model parameters of the coupling memristor. The memristor coupling neuron circuit fills the blank of research of using an N-type local active memristor coupling memristor neuron circuit in the prior art, and lays a certain foundation for application of the memristor coupling neuron circuit based on the N-type local active memristor in neuromorphic calculation.

Description

Technical Field

[0001] The present invention relates to the field of neuron circuit design, and in particular to a memristor-coupled neuron circuit based on an N-type local active memristor. Background Art

[0002] Neuromorphic computing uses biomimetic hardware to simulate the biological nervous system, enabling efficient, parallel information processing and storage. Memristor neurons combine the nonlinear properties of memristors with neuronal dynamics, faithfully recreating the learning and memory processes of biological neural systems. The coupling of memristors as synaptic elements to memristor neurons marks a shift in computing architecture from traditional neural networks to one more akin to biological neural systems.

[0003] Locally active memristor-coupled neuron circuits, with their unique nonlinear control properties, can generate rich dynamic behaviors, including complex oscillations. This provides a novel approach for simulating synaptic coupling mechanisms in biological neural networks and building efficient brain-inspired computing hardware. The edge of chaos, a subset of the locally active domain of a memristor, is stable but potentially unstable. Appropriate external perturbations can induce instability, leading to complex nonlinear dynamics. The mutual coupling between nonlinear systems holds significant research value in a wide range of applications.

[0004] There is no memristor-coupled neuron circuit based on N-type local active memristors in the prior art. Summary of the Invention

[0005] The present invention aims to solve the problems existing in the prior art and proposes a memristor-coupled neuron circuit based on an N-type local active memristor.

[0006] A memristive coupled neuron circuit based on an N-type local active memristor, characterized by comprising: two memristive neuron modules, each of the memristive neuron modules comprising a resistor, an inductor, and an N-type local active memristor connected in series; a capacitor connected in parallel at both ends of the N-type local active memristor;

[0007] In each of the memristive neuron modules, any point on the line connecting the resistor and the inductor is named as point p, and the points p of two memristive neuron modules are connected via a synaptic module composed of an N-type local active memristor.

[0008] In this circuit, two memristive neuron modules are coupled via a synaptic module composed of N-type locally active memristors, effectively simulating the synaptic connection between neurons and enabling dynamically adjustable synaptic weights. Under different parameter configurations, this structure can reproduce the Smale paradox phenomenon and demonstrate the dynamic characteristics of the transition from oscillation to chaos, demonstrating dynamic diversity and circuit plasticity.

[0009] Preferably, the two memristor neuron modules are named as the first memristor neuron module and the second memristor neuron module respectively; the first memristor neuron module includes: an N-type local active memristor 1, a DC voltage source V in1 , resistor R 1, , inductor L1 and capacitor C1; the DC voltage source V in1 The positive electrode of the N-type local active memristor is connected to one end of the resistor R1, the other end of the resistor R1 is connected to the input end of the inductor L1, the output end of the inductor L1 is connected to the positive electrode of the N-type local active memristor 1, the negative electrode of the N-type local active memristor 1 is connected to the ground, one end of the capacitor C1 is connected to the positive electrode of the N-type local active memristor 1, and the other end of the capacitor C1 is connected to the ground; the second memristive neuron module includes: an N-type local active memristor 2, a DC voltage source V in2 , resistor R 2, , inductor L2 and capacitor C2; DC voltage source V in2 The positive electrode of is connected to one end of the resistor R2, the other end of the resistor R2 is connected to the input end of the inductor L2, the output end of the inductor L2 is connected to the positive electrode of the N-type local active memristor 1, the negative electrode of the N-type local active memristor 2 is connected to the ground, one end of the capacitor C2 is connected to the positive electrode of the N-type local active memristor 2, and the other end of the capacitor C2 is connected to the ground.

[0010] Preferably, the positive electrode of the N-type local active memristor constituting the synaptic module is connected to the positive end of the inductor L1 , and the negative electrode is connected to the positive end of the inductor L2 .

[0011] Preferably, the mathematical models of the three N-type local active memristors included in the circuit are:

[0012]

[0013] Where i represents the current flowing through the N-type local active memristor and v represents the voltage across the N-type local active memristor, d2, d0, k, α0, α1, β1 represent independent constant parameters, x represents the state variable of the N-type local active memristor, and t represents time;

[0014] Each of the memristive neuron modules includes the same N-type local active memristor, that is, its constant parameters d2, d0, k, α0, α1, and β1 are consistent and are all expressed as d2, d0, k, α0, α1, β1.

[0015] Preferably, the N-type local active memristor constituting the synaptic module is also the same as the N-type local active memristor included in the memristive neuron module.

[0016] Preferably, the values of the constant parameters are as follows:

[0017] k = 1 × 10 4,d2=1.5×10 -4 ,d0=2.56×10 -4 ,α0=8,α1=-1,andβ1=-3.75.

[0018] Beneficial Effects: This invention proposes a memristor-coupled neuron circuit based on an N-type locally active memristor. N-type locally active memristors exhibit nonlinearity, overall passivity but local activity, and nanoscale dimensions. Therefore, compared with existing technologies, this neuron circuit can more accurately simulate the repolarization process of biological neurons and achieve dynamic behavior control that is difficult to trigger using traditional passive coupling, making it suitable for application in the field of neuromorphic computing. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Attachment Figure 1 The schematic diagram of the memristor-coupled neuron circuit based on N-type local active memristor; where v c1 、v c2 are the voltages across capacitors C1 and C2 in neuron 1 and neuron 2, respectively. x1 and x2 are the state variables of N-type local active memristor N-type LAM1 in neuron 1 and N-type local active memristor N-type LAM2 in neuron 2, respectively. L1 、i L2 are the currents flowing through the inductors L1 and L2 in the circuits of neuron 1 and neuron 2, respectively. i0 and x0 are the current and state variables of the N-type local active memristor N-type LAM0 in the synaptic module. i1 and i2 are the currents flowing through the resistors R1 and R2, respectively.

[0020] Attachment Figure 2 is the DC VI curve of the N-type local active memristor;

[0021] Attachment Figure 3 This is the time domain waveform diagram of the reproduction of the Smale paradox phenomenon before and after the coupling of two neurons in the memristor-coupled neuron circuit based on N-type local active memristor.

[0022] Attachment Figure 4 This is the time domain waveform diagram of the transition from oscillation to chaos before and after coupling of two neurons in a memristor-coupled neuron circuit based on N-type locally active memristors. DETAILED DESCRIPTION

[0023] The neuron circuit proposed in the present invention consists of three modules.

[0024] The first neuron module: DC voltage source V in1 , a resistor R 1, , an inductor L1 and a capacitor C1. DC voltage source V in1The positive electrode of is connected to one end of the resistor R1, the other end of the resistor R1 is connected to the input end of the inductor L1, the output end of the inductor L1 is connected to the positive electrode of the N-type local active memristor 1, the negative electrode of the N-type local active memristor 1 is connected to the ground, one end of the capacitor C1 is connected to the positive electrode of the N-type local active memristor 1, and the other end of the capacitor C1 is connected to the ground;

[0025] The second neuron module: DC voltage source V in2 , a resistor R 2, , an inductor L2 and a capacitor C2. DC voltage source V in2 The positive electrode of is connected to one end of the resistor R2, the other end of the resistor R2 is connected to the input end of the inductor L2, the output end of the inductor L2 is connected to the positive electrode of the N-type local active memristor 1, the negative electrode of the N-type local active memristor 2 is connected to the ground, one end of the capacitor C2 is connected to the positive electrode of the N-type local active memristor 2, and the other end of the capacitor C2 is connected to the ground;

[0026] Synaptic module: The positive electrode of the N-type local active memristor 0 is connected to the positive terminal of the inductor L1, and the negative electrode of the N-type local active memristor 0 is connected to the positive terminal of the inductor L2;

[0027] The mathematical models of the N-type local active memristor are:

[0028]

[0029] Where i and v represent the current and voltage flowing through the N-type local active memristor, g is the function of the state variable x and the voltage v, G M (x) is the memristor-valued function, f is a function of the state variable x and the voltage v, and d2, d0, k, α0, α1, and β1 are constants. In a memristor-coupled neuron circuit based on N-type locally active memristors, three memristors are introduced: N-type LAM1, N-type LAM2, and N-type LAM0. The model parameters of N-type LAM1 and N-type LAM2 are identical, both described by d2, d0, k, α0, α1, and β1. To distinguish them, the coupled memristor, N-type LAM0, introduces a separate set of independent parameters, denoted as d2', d0', k', α0', α1', and β1', to reflect its different memristive properties.

[0030] The present invention will be further described below in conjunction with the accompanying drawings:

[0031] like Figure 1 The figure shows a memristor coupled neuron circuit based on N-type local active memristor, which consists of three modules: the first neuron module (neuron 1 in the figure): a DC voltage source V in1 , a resistor R 1,, an inductor L1 and a capacitor C1. DC voltage source V in1 The positive electrode of is connected to one end of the resistor R1, the other end of the resistor R1 is connected to the input end of the inductor L1, the output end of the inductor L1 is connected to the positive electrode of the N-type local active memristor 1, the negative electrode of the N-type local active memristor 1 is connected to the ground, one end of the capacitor C1 is connected to the positive electrode of the N-type local active memristor 1, and the other end of the capacitor C1 is connected to the ground; the second neuron module (neuron 2 in the figure): is connected by a DC voltage source V in2 , a resistor R 2, , an inductor L2 and a capacitor C2. DC voltage source V in2 The positive electrode of is connected to one end of the resistor R2, the other end of the resistor R2 is connected to the input end of the inductor L2, the output end of the inductor L2 is connected to the positive electrode of the N-type local active memristor 1, the negative electrode of the N-type local active memristor 2 is connected to the ground, one end of the capacitor C2 is connected to the positive electrode of the N-type local active memristor 2, and the other end of the capacitor C2 is connected to the ground; synaptic module: the positive electrode of the N-type local active memristor 0 is connected to the positive end of the inductor L1, and the negative electrode of the N-type local active memristor 0 is connected to the positive end of the inductor L2;

[0032] The process of establishing the mathematical model of the N-type local active memristor includes the following steps:

[0033] Step 1: According to Chua's expansion theorem, the mathematical model of a general voltage-controlled memristor is:

[0034]

[0035] Where i, v, and x are the current flowing through the memristor, the voltage across the memristor, and the state variable of the memristor, respectively. M (x) is the memetic derivative function, f is the function of the state variable x and the voltage v, α k ,β k ,δ kl ,d k are the expansion coefficients; r1, r2, n1, n2, m1, m2, p1, p2, q1, and q2 represent the lowest and highest powers of the variables, respectively; k and l represent the kth and lth powers of the variables, respectively. f(x, v) is a function of x and v.

[0036] Step 2: The state variable equation of the N-type local active memristor proposed by the present invention is:

[0037]

[0038] Here, k is used to change the rate of change of the state variable of the memristor, thereby affecting the operating frequency range of the memristor.

[0039] Step 3: Let formula (3) equal to 0, when the bias voltage v = V

[0040]

[0041] Step 4: Substitute equation (4) into equation (3), and the current-voltage relationship of the N-type locally active memristor at the stable operating point can be obtained as follows:

[0042]

[0043] Step 5: According to equation (5), a simple mathematical model of the N-type locally active memristor can be obtained as

[0044]

[0045] Using the general circuit analysis method and the mathematical model of the N-type locally active memristor, the state equation of the neuron circuit in the appendix can be obtained Figure 1 in the appendix

[0046]

[0047] where the parameters of the mathematical model are set as k = k' = 1×10 4 , d2 = d2 ' = 1.5×10 -4 , d0 = d0 ' = 2.56×10 -4 , α0 = α0 ' = 8, α1 = α1 ' = -1, and β1 = β1 ' = -3.75. When the DC voltage source is increased from 0V to 3.5V in steps of 0.1V, the DC V-I curve in the appendix is obtained. It is observed that the obtained DC V-I curve exhibits negative differential resistance (NDR) characteristics in a specific region, where 0.85V < V < 2.41V and 0.61mA < I < 4.53mA. Based on the local activity theory, when the DC bias voltage is within the range of (0.85V, 2.41V), the N-type LAM under this parameter may cause oscillations. Figure 2

[0048] <![CDATA[When in the memristor-coupled neuron circuit, V]]> in1 <![CDATA[ = V]]> in2 <![CDATA[ = 2V, C1 = C2 = 50nF, L1 = L2 = 41mH, R1 = R2 = 100Ω, and the initial conditions are [x1, v]]> c1 <![CDATA[, i]]> L1 <![CDATA[, x2, v]]> c2 <![CDATA[, i]]> L2 <![CDATA[]]>,x3]=[1,0,0,-1,0,0,1], and the three memristor parameters are selected as k=k'=1×10 4 ,d2=d2 ' =1.5×10 -4 ,d0=d0 ' =2.56×10 -4 ,α0=α0 ' =8,α1=α1 ' =-1,andβ1=β1 ' = -3.75, the two memristor neurons first undergo periodic decay oscillation, then gradually transform into amplification oscillation, and finally maintain a continuous oscillation state. Figure 3 The time domain waveforms of the Smale paradox phenomenon before and after the two neurons are coupled are shown. in1 =V in2 =2V,C1=C2=50nF,L1=L2=41mH,R1=R2=100Ω, initial conditions [x1,v c1 ,i L1 ,x2,v c2 ,i L2 ,x3]=[1,0,0,-1,0,0,1], and the three memristor parameters are selected as k=k'=2×10 4 ,d2=d2 ' =1.5×10 -4 ,d0=d0 ' =2.56×10 -4 ,α0=α0 ' =8,α1=α1 ' =-1,andβ1=β1 ' = -3.75, the neural network can change from oscillation to chaos state, and the additional Figure 4 The time-domain waveforms of the transition from oscillation to chaos before and after the coupling of two neurons are shown. This further illustrates that the introduction of N-type locally active memristors overcomes the limitations of traditional passive memristor coupling methods and reveals the key role of coupled memristor parameters in the dynamic characteristics of control systems, providing a solid theoretical basis for further research into the complex dynamics of memristive systems. Compared to existing technologies, this neuronal circuit can more accurately simulate the repolarization process of biological neurons and achieve dynamic behavior control that is difficult to trigger with traditional passive methods, making it suitable for use in the field of neuromorphic computing.

Claims

1. A memristor-coupled neuron circuit based on an N-type local active memristor, characterized in that: include: Two memristive neuron modules, each comprising a resistor, an inductor, and an N-type local active memristor connected in series; a capacitor is connected in parallel at both ends of the N-type local active memristor; In each of the memristive neuron modules, any point on the line connecting the resistor and the inductor is named as point p, and the points p of two memristive neuron modules are connected via a synaptic module composed of an N-type local active memristor.

2. A memristor-coupled neuron circuit based on an N-type local active memristor according to claim 1, characterized in that: The two memristor neuron modules are named the first memristor neuron module and the second memristor neuron module respectively; The first memristor neuron module includes: an N-type local active memristor 1, a DC voltage source V in1 , resistor R 1, , inductor L1 and capacitor C1; the DC voltage source V in1 The positive electrode of is connected to one end of the resistor R1, the other end of the resistor R1 is connected to the input end of the inductor L1, the output end of the inductor L1 is connected to the positive electrode of the N-type local active memristor 1, the negative electrode of the N-type local active memristor 1 is connected to the ground, one end of the capacitor C1 is connected to the positive electrode of the N-type local active memristor 1, and the other end of the capacitor C1 is connected to the ground; The second memristor neuron module includes: an N-type local active memristor 2, a DC voltage source V in2 , resistor R 2, , inductor L2 and capacitor C2; DC voltage source V in2 The positive electrode of is connected to one end of the resistor R2, the other end of the resistor R2 is connected to the input end of the inductor L2, the output end of the inductor L2 is connected to the positive electrode of the N-type local active memristor 1, the negative electrode of the N-type local active memristor 2 is connected to the ground, one end of the capacitor C2 is connected to the positive electrode of the N-type local active memristor 2, and the other end of the capacitor C2 is connected to the ground.

3. The memristor-coupled neuron circuit based on an N-type local active memristor according to claim 2, characterized in that: The positive electrode of the N-type local active memristor constituting the synaptic module is connected to the positive end of the inductor L1 , and the negative electrode thereof is connected to the positive end of the inductor L2 .

4. The memristor-coupled neuron circuit based on an N-type local active memristor according to claim 1, characterized in that: The mathematical models of the three N-type local active memristors included in the circuit are: Where i represents the current flowing through the N-type local active memristor and v represents the voltage across the N-type local active memristor, d2, d0, k, α0, α1, β1 represent independent constant parameters, x represents the state variable of the N-type local active memristor, and t represents time; Each of the memristive neuron modules includes the same N-type local active memristor, that is, its constant parameters d2, d0, k, α0, α1, and β1 are consistent and are all expressed as d2, d0, k, α0, α1, β1.

5. A memristor-coupled neuron circuit based on an N-type local active memristor according to claim 4, characterized in that: The N-type local active memristor constituting the synaptic module is also the same as the N-type local active memristor included in the memristive neuron module.

6. A memristor-coupled neuron circuit based on an N-type local active memristor according to claim 5, characterized in that: The values of the constant parameters are as follows: k=1×10 4 ,d2=1.5×10 -4 ,d0=2.56×10 -4 ,α0=8,α1=-1,andβ1= -3.75。

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