Composite memristive synaptic coupling neural network discharge regulation and control method

Abstract

A composite memristive synapse coupled neural network discharge behavior regulation and control method comprises the following steps: step 1, designing a multistable memristor, and connecting the multistable memristor with a resistor in series to construct a composite memristive synapse; 2, analyzing the adjusting effect of the series resistor on the composite memristor synaptic dynamic path diagram and the influence of the series resistor on the memristor balance point offset speed; 3, constructing a composite memristor synaptic coupling neural network, and analyzing the influence of series resistance on the balance point dynamics of the neural network; 4, drawing a bifurcation diagram about the series resistance, and analyzing the regulation and control effect of the series resistance on the discharge behavior of the coupled neural network; 5, constructing a neural network model in which the memristor balance point offset speed is not controlled by the series resistor, comparing the neural network model with the model in the step 3, and analyzing the influence of the memristor balance point offset speed on the discharge behavior of the neural network; and step 6, designing a composite memristor synaptic coupling neural network discharge behavior regulation and control method based on the influence of the series resistors on the offset speed of the composite memristor synaptic equilibrium point.

Description

Technical Field

[0001] The present invention relates to a method for regulating discharge behavior of a composite memristor synapse coupled neural network. Background Art

[0002] Memristors are nonvolatile, plastic, nanoscale, and nonlinear devices. Their existence was confirmed by HP Labs in 2008. In recent years, they have been widely used in various fields, including circuits, storage, and computing. Particularly noteworthy is their biomimetic properties, making them ideal for simulating biological synapses and electromagnetic radiation, and they are often used to construct various memristive neural networks.

[0003] Despite extensive research on the discharge behavior of memristive neural networks, these systems are typically strongly nonlinear, and their structural complexity poses significant challenges to identifying discharge parameters and regulating discharge behavior. Bifurcation mechanism methods primarily analyze the local stability of the system, exploring the relationship between equilibrium stability and discharge modes, and studying the discharge activity of neural system models from a nonlinear dynamics perspective. However, since bifurcation mechanism methods only consider the influence of slowly varying parameters on the local stability of the system, it is difficult to determine how the actual parameters of the neural system model and the coupling parameters regulate the discharge behavior.

[0004] Local activity refers to the negative slope of the voltage-current characteristic curve of a two-port element or network at one or more operating points. Local activity theory determines the chaotic edge and discharge parameter conditions of neural systems by analyzing the asymptotic stability and local activity at these operating points. Therefore, research methods based on local activity theory primarily explore the emergent conditions of neural system discharge activity from the perspective of the origin of complexity. However, this method cannot determine the switching of discharge modes and the evolution of discharge behavior in the chaotic edge region. Furthermore, because neuron models lack clear input and output ports, local activity theory faces difficulties in practical applications of memristive neural networks. In summary, current research methods for regulating the discharge behavior of memristive neural networks have certain limitations. Summary of the Invention

[0005] Based on the problems existing in the current research methods for regulating the discharge behavior of memristive neural networks, this application proposes a discharge regulation method for a composite memristive synaptic coupled neural network, which specifically includes the following steps:

[0006] Step 1: Design a multistable memristor and couple it in series with a resistor to construct a composite memristor synapse. Establish the descriptive equation of the composite memristor synapse and its connection with the multistable memristor.

[0007] Step 2: Analyze the regulatory effect of the series resistor on the dynamic path diagram of the composite memristor synapse and determine its influence on the offset speed and resistance value of the memristor equilibrium point;

[0008] Step 3: Construct a memristive neural network based on composite memristive synaptic coupling and analyze the effect of series resistance on the geometric distribution of the neural network equilibrium point and the dynamic characteristics;

[0009] Step 4: Write a Matlab program, select the appropriate Poincare cross section, draw a bifurcation diagram for the series resistance value, analyze the discharge behavior of the memristive neural network under different series resistance values, and analyze the regulation of the series resistance on the discharge behavior of the memristive neural network;

[0010] Step 5: Construct a model in which the memristor equilibrium point offset speed is not controlled by the series resistance. This model is used to compare with the model in step 3 and analyze the impact of the memristor equilibrium point offset speed on the discharge behavior of the neural network.

[0011] Step 6: Based on the influence of series resistance on the offset speed and resistance value of the composite memristor synapse equilibrium point, a method for regulating the discharge behavior of composite memristor synapse coupled neural network based on the principle of energy transfer and balance is designed.

[0012] As a further solution of the present invention: a solution for constructing a composite memristive synapse based on a memristor coupled in series with a resistor includes the following steps:

[0013] Step 1: Construct a universal voltage-controlled memristor M model in a composite memristor synapse

[0014]

[0015] v and i represent the input voltage and output current of the memristor M, respectively. w(x) represents the memristor function of the memristor M. x represents the internal state variable of M. is the time derivative of x. The function f(x) is used to describe the change process of the internal state variable x. a and b are the parameters of the memristor.

[0016] Step 2: Connect the resistor R in series with the memristor and apply an external excitation voltage v s Based on Kirchhoff's law, the constructed circuit is analyzed to obtain the internal state variable equation of the composite memristor synapse

[0017]

[0018] Let v m is the control voltage of the memristor, and its external equation is expressed as:

[0019] i s =w(x)·v m

[0020] i s The applied voltage v m The current of the memristor M is .

[0021] Step 3: Set v m Replaced by external stimulus v of composite memristor synapse s At this time, the synaptic current is controlled by the excitation voltage and the total resistance of the composite memristive synapse. Based on Ohm's law, the external equation expression of the composite memristive synapse can be obtained:

[0022] i s =(w(x) -1 +R) -1 v s

[0023] In summary, the expression of the composite memristive synapse is:

[0024]

[0025] At this time, the internal state equation of the composite memristor synapse is related to the resistance, and the resistance value can affect the change speed of the state variable x, thereby causing a change in the offset speed of the memristor equilibrium point.

[0026] As a further solution of the present invention: Taking HR neurons and tabu neurons as examples, the composite memristor synaptic coupled neural network is

[0027]

[0028] Where x1 and y1 represent the membrane potential and recovery variable of HR neurons, a1, b1, c1, and d1 are the parameters of HR neurons; x2 and y2 represent the membrane potential and recovery variable of tabu neurons, a2, b2, c2, and d2 are the parameters of tabu neurons, and f2(x2) = 2tanh(5.2x2)-tanh(5.2x2+7.8)-tanh(5.2x2-7.8) is the activation function of tabu neurons; I1 and I2 is the external excitation current of HR neurons and tabu neurons, k is the synaptic coupling parameter; x is the internal state variable of the memristor, f(x) = xg(100(x+1))-g(100(x-1))+g(100(x+3))-g(100(x-3)) is the function describing the change process of the internal state variable x (where g(x) = x(|x|+1)-1), w(x) = |x| is the memristor's memristor function, and a and b are the parameters of the memristor.

[0029] As a further solution of the present invention: a neural network model with uncontrolled memristor equilibrium point based on a composite memristor synaptic coupled neural network

[0030]

[0031] Compared with the existing technology, the present invention has the following advantages: a memristor is coupled in series with a resistor to form a composite memristive synapse. Through the voltage divider effect of the resistor, the offset speed of the composite memristive synapse's equilibrium point is controlled, thereby regulating the discharge behavior of the neural network.

[0032] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The drawings described below are only some embodiments of the present invention. Those skilled in the art can derive other drawings based on these drawings without creative work.

[0034] Figure 1 This is a circuit diagram for building a composite memristor synapse.

[0035] Figure 2 This is the dynamic path diagram of the memristive synapse.

[0036] Figure 3 The dynamic path diagram of the composite memristive synapse.

[0037] Figure 4 This is the structural diagram of the designed memristive neural network.

[0038] Figure 5 Bifurcation diagram of the memristive neural network variable x1 with respect to the resistance R when the equilibrium point is controlled and uncontrolled, (a) x(0) = 0.1.

[0039] Figure 6 Bifurcation diagram of the memristive neural network variable x1 with respect to the resistance R when the equilibrium point is controlled and uncontrolled, (b) x(0) = 2.

[0040] Figure 7 The bifurcation diagram of the memristive neural network variable x1 with respect to the resistance R when the equilibrium point is controlled.

[0041] Figure 8 The bifurcation diagram of the uncontrolled memristor neural network variable x1 with respect to the resistor R.

[0042] Figure 9 The bifurcation diagram of the memristive neural network variable x with respect to the resistance R when the equilibrium point is controlled.

[0043] Figure 10 This is the bifurcation diagram of the memristor neural network variable x with respect to the resistance R when the equilibrium point is uncontrolled.

[0044] Figure 11 Schematic diagram of the discharge control method of composite memristor synapse coupled neural network. DETAILED DESCRIPTION

[0045] The following is a clear and complete description of the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0046] See also Figures 1 to 10 In an embodiment of the present invention, a method for controlling the discharge behavior of a memristor neural network based on the regulation of the memristor equilibrium point offset speed includes the following steps:

[0047] Step 1: Design a multistable memristor and couple it in series with a resistor to construct a composite memristor synapse. Establish the descriptive equation of the composite memristor synapse and its connection with the multistable memristor.

[0048] Step 2: Analyze the regulatory effect of the series resistor on the dynamic path diagram of the composite memristor synapse and determine its influence on the offset speed and resistance value of the memristor equilibrium point;

[0049] Step 3: Construct a memristive neural network based on composite memristive synaptic coupling and analyze the effect of series resistance on the geometric distribution of the neural network equilibrium point and the dynamic characteristics;

[0050] Step 4: Write a Matlab program, select the appropriate Poincare cross section, draw a bifurcation diagram for the series resistance value, analyze the discharge behavior of the memristive neural network under different series resistance values, and analyze the regulation of the series resistance on the discharge behavior of the memristive neural network;

[0051] Step 5: Construct a model in which the offset speed of the memristor equilibrium point is not controlled by the series resistance. This model is used for comparison with the model in step 3. The influence of the offset speed of the memristor equilibrium point on the discharge behavior of the neural network is analyzed based on methods such as bifurcation diagrams, discharge timing diagrams, and dynamic path diagrams.

[0052] Step 6: Based on the influence of series resistance on the offset speed and resistance value of the composite memristor synapse equilibrium point, a method for regulating the discharge behavior of composite memristor synapse coupled neural network based on the principle of energy transfer and balance is designed.

[0053] As a further solution of the present invention: in step 1, the construction scheme of the composite memristor synapse based on the coupling of a memristor and a resistor includes the following steps:

[0054] Step 1: Construct a general voltage-controlled memristor model for building composite memristive synapses

[0055]

[0056] Where v and i represent the input voltage and output current of the memristor M, respectively; w(x) represents the memristor M’s memristor function; and x represents the internal state variable of M. is the time derivative of x. The function f(x) is used to describe the change process of the internal state variable x. a and b are the parameters of the memristor.

[0057] Step 2: Connect the resistor R in series with the memristor M and apply an external excitation voltage v s Based on Kirchhoff's law, the constructed circuit is analyzed to obtain the internal state variable equation of the composite memristor synapse

[0058]

[0059] Let v m is the control voltage of the memristor, and its external equation is expressed as:

[0060] i s =w(x)·v m

[0061] i s The applied voltage v m The current of the memristor M is .

[0062] Step 3: Set v m Replaced by external stimulus v of composite memristor synapse s At this time, the synaptic current is controlled by the excitation voltage and the total resistance of the composite memristive synapse. Based on Ohm's law, the external equation expression of the composite memristive synapse can be obtained:

[0063] i s =(w(x) -1 +R) -1 v s

[0064] In summary, the expression of the composite memristive synapse is:

[0065]

[0066] At this point, the internal state equation of the composite memristor synapse is related to the series resistance, which can affect the rate of change of the state variable x, thereby causing a change in the rate of offset of the memristor equilibrium point. The series coupling resistance can change the dynamic path diagram of the composite memristor synapse, allowing the synapse to produce different effects during neuronal energy exchange. The dynamic path diagrams of the memristor synapse and composite memristor synapse are shown in Figure 1. Figure 2 、 3 shown.

[0067] As a further solution of the present invention: Taking HR neurons and tabu neurons as examples, the composite memristor synaptic coupled neural network is

[0068]

[0069] Where x1 and y1 represent the membrane potential and recovery variable of HR neurons, a1, b1, c1, and d1 are the parameters of HR neurons; x2 and y2 represent the membrane potential and recovery variable of tabu neurons, a2, b2, c2, and d2 are the parameters of tabu neurons, and f2(x2) = 2tanh(5.2x2)-tanh(5.2x2+7.8)-tanh(5.2x2-7.8) is the activation function of tabu neurons; I1 and I2 is the external excitation current of HR neurons and tabu neurons, k is the synaptic coupling parameter; x is the internal state variable of the memristor, f(x)=xg(100(x+1))-g(100(x-1))+g(100(x+3))-g(100(x-3)) is the function describing the change process of the internal state variable x (where g(x)=x(|x|+1)-1), w(x)=|x| is the memristor's memristor function, and a and b are the parameters of the memristor. The network model diagram is shown in Figure 4 Adjusting the parameters of the composite memristor synapse can change the discharge behavior of the memristor neural network, and the discharge behavior is different under different initial value conditions. Compared with the memristor synapse, the composite memristor synapse can make the neural network produce richer multistable behaviors.

[0070] When a1=1, b1=3, c1=1, d1=5, a2=0.2, b2=0.3, c2=0.5, d2=1, I1=I2=0, k=2, a=-1.35, b=1.7, the bifurcation diagrams of the memristor neural network with respect to the resistor R under different initial values ​​are shown as follows: Figure 5 、 6 shown.

[0071] As a further solution of the present invention: the neural network model in which the memristor equilibrium point is uncontrolled in the discharge behavior control method of the composite memristor synaptic coupled neural network is

[0072]

[0073] When the offset speed of the memristor equilibrium point changes, the neural network will produce different discharge behaviors. In order to better analyze the impact of the equilibrium point offset speed on the discharge behavior of the neural network, the discharge behavior bifurcation diagram of the memristor neural network variable x1 with respect to the resistor R is drawn in the two cases of controlled and uncontrolled equilibrium points. Figure 7 、 8 As shown in the figure, the bifurcation diagram of the discharge behavior of the memristor state variable x with respect to the resistor R in the memristor neural network is shown in the figure. Figure 9 、 10 As shown. Figure 7 、 8It can be seen that when the memristor equilibrium point is controlled by the resistor R, the bifurcation change of the neural network variable x1 becomes slower; when the memristor equilibrium point is not controlled by the resistor R, the bifurcation diagram state switching speed of x1 is faster. Figure 9 、 10 It can be seen that when the memristor equilibrium point is not controlled by resistor R, the memristor state variable x is distributed near multiple memristor equilibrium points. When the memristor equilibrium point is controlled by resistor R, x is mainly distributed in the equilibrium point region corresponding to the current initial value. Therefore, resistor R slows down the offset of the memristor equilibrium point and can effectively regulate the discharge behavior of the neural network.

[0074] like Figure 11 As shown, the method of the present application includes the following steps: Step 1: Design a multistable memristor and construct a composite memristive synapse in series with a resistor; Step 2: Analyze the regulatory effect of the series resistor on the dynamic path diagram of the composite memristive synapse and the influence on the equilibrium point offset speed of the memristor; Step 3: Construct a neural network coupled with the composite memristive synapse, and analyze the influence of the series resistor on the equilibrium point dynamics of the neural network; Step 4: Draw a bifurcation diagram about the series resistor, and analyze the regulatory effect of the series resistor on the discharge behavior of the coupled neural network; Step 5: Construct a neural network model in which the equilibrium point offset speed of the memristor is not controlled by the series resistor, compare it with the model in Step 3, and analyze the influence of the equilibrium point offset speed of the memristor on the discharge behavior of the neural network; Step 6: Based on the influence of the series resistor on the equilibrium point offset speed of the composite memristive synapse, design a method for regulating the discharge behavior of the composite memristive synapse coupled neural network.

[0075] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

Claims

1. A method for regulating the discharge behavior of a composite memristor synaptic coupled neural network, characterized by: A composite memristive synapse is constructed by connecting series resistors. The series resistors are used to adjust the offset speed of the composite memristive synapse's equilibrium point under the same applied voltage, while also adjusting its resistance and energy transfer capacity, thereby effectively regulating the discharge behavior of the memristive coupled neural network. This scheme includes the following steps: Step 1: Design a multistable memristor and couple it in series with a resistor to construct a composite memristor synapse. Establish a mathematical description equation for the composite memristor synapse and its connection with the multistable memristor. Step 2: Analyze the regulatory effect of the series resistor on the dynamic path diagram of the composite memristor synapse and determine its influence on the offset speed and resistance value of the memristor equilibrium point; Step 3: Construct a memristive neural network based on composite memristive synaptic coupling and analyze the effect of series resistance on the geometric distribution of the neural network equilibrium point and the dynamic characteristics; Step 4: Write a Matlab program, select the appropriate Poincare cross section, draw a bifurcation diagram for the series resistance value, analyze the discharge behavior of the memristive neural network under different series resistance values, and analyze the regulation of the series resistance on the discharge behavior of the memristive neural network; Step 5: Construct a model in which the memristor equilibrium point offset speed is not controlled by the series resistance. This model is used to compare with the model in Step 3 and analyze the impact of the memristor equilibrium point offset speed on the discharge behavior of the neural network. Step 6: Based on the influence of series resistance on the offset speed and resistance value of the composite memristor synapse equilibrium point, a method for regulating the discharge behavior of composite memristor synapse coupled neural network based on the principle of energy transfer and balance is designed.

2. The method for regulating discharge behavior of a composite memristor synaptic coupled neural network according to claim 1, characterized in that: The offset speed of the composite memristive synapse equilibrium point under the same applied voltage can be changed by adjusting the series resistance. In step 1, the steps for constructing the composite memristive synapse are as follows: Step 1: Construct a model of a universal voltage-controlled memristor M for building a composite memristive synapse v and i represent the input voltage and output current of the memristor M, respectively. w(x) represents the memristor's memristor function. x is the internal state variable of the memristor. is the time derivative of x, f(x) = xg(100(x+1)) - g(100(x-1)) + g(100(x+3)) - g(100(x-3)) is the function describing the change process of the internal state variable x (where g(x) = x(|x|+1) - 1), w(x) = |x| is the memristor's memristor function, and a and b are the parameters of the memristor.

3. The method for regulating discharge behavior of a composite memristor synaptic coupled neural network according to claim 1, characterized in that: Step 2: Connect the resistor R in series with the memristor M, and analyze the constructed circuit by applying an external excitation voltage and based on Kirchhoff's law to obtain the internal state variable equation of the composite memristor synapse Let v m is the control voltage of the memristor, and its external equation is expressed as: i s =w(x)·v m 。 i s The applied voltage v m The current of the memristor M is .

4. The method for regulating discharge behavior of a composite memristor synaptic coupled neural network according to claim 1, characterized in that: Step 3: Set v m Replaced by external stimulus v of composite memristor synapse s At this time, the synaptic current is controlled by the excitation voltage and the total resistance of the composite memristive synapse. Based on Ohm's law, the external equation expression of the composite memristive synapse can be obtained: i s =(w(x) -1 +R) -1 v s In summary, the expression of the composite memristive synapse is: The internal state equation of the composite memristor synapse is related to the resistance. The resistance value can affect the change speed of the state variable x, which in turn leads to a change in the offset speed of the memristor equilibrium point.

5. The method for regulating discharge behavior of a composite memristor synaptic coupled neural network according to claim 4, characterized in that: The discharge characteristics of the memristive neural network constructed based on the composite memristive synapse can be adjusted by adjusting the size of the series resistor R. In the step 3, taking the composite memristive synapse coupled HR neuron and tabu neuron as an example, the constructed memristive neural network is as follows: Where x1 and y1 represent the membrane potential and recovery variable of the HR neuron, and a1, b1, c1, and d1 are the parameters of the HR neuron; x2 and y2 represent the membrane potential and recovery variable of the tabu neuron, and a2, b2, c2, and d2 are the parameters of the tabu neuron; f2(x2) = 2tanh(5.2x2)-tanh(5.2x2+7.8)-tanh(5.2x2-7.8) is the activation function of the tabu neuron; I1 and I2 are the external excitation currents of the HR neuron and the tabu neuron, and k is the synaptic coupling parameter.

6. The method for regulating discharge behavior of a composite memristor synaptic coupled neural network according to claim 1, characterized in that: By establishing a neural network model in which the offset speed of the memristor equilibrium point is not controlled by the series resistance, the role of the dynamic offset of the memristor equilibrium point in the discharge process of the neural network is further explored; in the step 5, the neural network model in which the memristor equilibrium point is not controlled is When constructing a memristor neural network model with an uncontrolled memristor equilibrium point, based on the original memristor neural network architecture, the direct regulation function of the series resistor in the composite memristor synapse on the memristor state was removed, but the role of the resistor in energy transfer between neurons was retained. The purpose is to specifically analyze how changes in the memristor state independently affect the discharge behavior of the neural network.

Images