Discrete neuron system coupled with memristor with controllable discharge mode

Abstract

The application discloses a discharge mode controllable memristor coupling discrete neuron system, which comprises three delay units U1, U2 and U3, an invariable parameter C2, variable parameters C1, C3, C4, C5 and C6, a hyperbolic tangent module T, a square module S, multipliers M1, M2 and M3, a divider D, adders A1, A2, A3, A4 and A5, and three outputs X, Y and Z. A magnetic control memristor is introduced into a Rulkov discrete neuron, and corresponding parameters are adjusted, so that the system exhibits complex dynamic behaviors. By changing the initial value and the corresponding parameters of the system, the system exhibits transient chaotic discharge, transient periodic discharge, intermittent chaotic discharge, coexistence of periodic and chaotic discharge modes, discharge mode transition and other phenomena, and has multi-stability. The discharge mode controllable memristor coupling discrete neuron system provides a new idea for the development of neural dynamics, intelligent control, bionics and discrete neurons, provides theoretical guidance for the research on discrete neurons in medical experiments, and promotes the development of nonlinear dynamics of the memristor coupling discrete neuron direction.

Description

Technical Field

[0001] This invention pertains to memristor-based neurodynamic systems. Specifically, it involves introducing a magnetically controlled memristor for coupling within a discrete neuron system, thereby constructing a memristor-coupled discrete neuron system with controllable discharge modes. By adjusting the corresponding system parameters, a variety of dynamic behaviors can be obtained. Background Technology

[0002] Neurons are the basic units constituting the nervous system, and their firing activity plays a crucial role in information processing and intelligent control. Experiments with biological neurons have confirmed the existence of chaotic phenomena, and the established mathematical models exhibit similar dynamic characteristics and firing patterns to those observed in biological cell and tissue membrane potential experiments. Memristors, possessing nonlinear, nanoscale, and non-volatile properties, are natural nonlinear elements used to simulate biological synapses, while also reducing power consumption in neural circuits. The feasibility of this approach has been demonstrated in continuous neurons, revealing abundant dynamic phenomena and possessing broad potential application value.

[0003] A memristor-coupled discrete neuron system with controllable firing modes exhibits different firing modes under different system parameters, displaying complex dynamic phenomena. This invention can be implemented using general-purpose electronic devices, providing new ideas for the development of neural dynamics, intelligent control, bionics, and discrete neurons. It offers theoretical guidance for the study of discrete neurons in medical experiments and promotes the development of nonlinear dynamics in memristor-coupled discrete neurons. Summary of the Invention

[0004] The technical problem to be solved by this invention is to realize a memristor-coupled discrete neuron system with controllable firing modes.

[0005] To address the aforementioned technical problems, this invention provides a memristor-coupled discrete neuron system with controllable firing modes. For example... Figure 1 It includes three delay units U1, U2, U3, an invariant parameter C2, variable parameters C1, C3, C4, C5, C6, a hyperbolic tangent module T, a squaring module S, multipliers M1, M2, M3, a divider D, adders A1, A2, A3, A4, A5, and three outputs X, Y, Z.

[0006] The specific connection method is as follows:

[0007] Figure 1The second terminal of the delay unit U1 is connected to the first terminal of the squaring module S, the third terminal of the multiplier M1, the "+" terminal of the adder A2, and the first terminal of the multiplier M3; the variable parameter C3 is connected to the second terminal of the multiplier M3, and the third terminal of the multiplier M3 is connected to the first "+" terminal of the adder A5; the second terminal of the squaring module S is connected to the second "+" terminal of the adder A1, the invariant parameter C2 is connected to the first "+" terminal of the adder A1, the third terminal of the adder A1 is connected to the "÷" terminal of the divider D, the variable parameter C1 is connected to the "×" terminal of the divider D, and the third terminal of the divider D is connected to the first "+" terminal of the adder A3; the variable parameter C4 is connected to the first terminal of the multiplier M1, and the second terminal of the hyperbolic tangent module T is connected to the second terminal of the multiplier M1. The hyperbolic tangent module T is connected to the second "+" terminal of adder A5 and the second terminal of delay unit U3. The fourth terminal of multiplier M1 is connected to the second "+" terminal of adder A3. The variable parameter C5 is connected to the "-" terminal of adder A2. The third terminal of adder A2 is connected to the second terminal of multiplier M2. The variable parameter C6 is connected to the first terminal of multiplier M2. The third terminal of multiplier M2 is connected to the "-" terminal of adder A4. The second terminal of delay unit U2 is connected to the "+" terminal of adder A4 and the third "+" terminal of adder A3. The fourth terminal of adder A3 is connected to the first terminal of delay unit U1. The third terminal of adder A4 is connected to the first terminal of delay unit U2. The third terminal of adder A5 is connected to the first terminal of delay unit U3.

[0008] The model of the magnetically controlled memristor used in this invention is as follows:

[0009]

[0010] In the formula, W(φ(n)) is the memconductance, i and v are the DC current and DC voltage, respectively, f(φ(n)) is the internal state function of the memristor, and α, β, and γ are the memristor parameters;

[0011] The aforementioned magnetically controlled memristor is coupled to a Rulkov neuron.

[0012]

[0013] Where a, μ, and σ are Rulkov neuron parameters, 0 < μ < < 1, x(n) is the membrane potential energy, k is the coupling coefficient, a and σ control the neuron's firing state, and ε is the system parameter.

[0014] The Simulink simulation model parameters were selected as follows: C1 = 4.15, C3 = 1, C5 = -1.2, C6 = 0.00001. When the initial values ​​U1 = 0.1, U2 = 0.1, and U3 = 0.1, the system is always in a periodic discharge state. As shown in Figures 2(a)-(b) under these conditions, the MATAB numerical simulation results show a period-doubling bifurcation phenomenon. When the initial values ​​U1 = 0.1, U2 = -2.75, and U3 = -2, the system is in a discharge state where periodicity and chaos coexist. As shown in Figures 2(c)-(d) under these conditions, the bifurcation diagram shows a phenomenon of transitioning from chaos to periodicity and then from periodicity to chaos. The results indicate that the bifurcation path is closely related to the initial values.

[0015] The Simulink simulation model parameters were selected as follows: C1 = 4.5, C3 = 1, C4 = 0.5, C5 = -1.2, C6 = 0.0001. When the initial values ​​were U1 = 0.1, U2 = -2.75, and U3 = 0.1, Figure 3(a) shows the MATAB numerical simulation results under these conditions. The time series diagram of system x shows a transient chaotic discharge phenomenon. When the initial values ​​were U1 = 0.1, U2 = -2.65, and U3 = 1, Figure 3(b) shows the MATAB numerical simulation results under these conditions. The time series diagram of system x shows a transient periodic discharge phenomenon.

[0016] The Simulink simulation model parameters were selected as follows: C1 = 4.5, C3 = 1, C5 = -1.2, C4 = 0.7, C6 = 0.001. When the initial values ​​were U1 = 0.1, U2 = -2.85, U3 = 0.1 or U1 = 0.1, U2 = -2.75, U3 = 0.1, the MATAB numerical simulation results under these conditions are shown in Figures 4(a)-(b). The time series diagrams of the corresponding system x show the intermittent chaotic discharge phenomenon. The phenomenon is not completely the same for different initial values.

[0017] The Simulink simulation model parameters are selected as follows: C1 = 4.15, C3 = 1, C5 = -1.2, C6 = 0.00001. The initial values ​​are U1 = 0.1, U2 = -2.75, U3 = 0.1. When C4 = 0.5, the transition between periodic and chaotic discharge modes can be performed; for example... Figure 5 Figures 6(a)-(b) show the MATAB numerical simulation results under these conditions, corresponding to the bifurcation diagram of system x with respect to φ(0) and the time series diagram of x. Figure 5 It can be observed that φ(0) = 0.7 is the critical point for the transition between periodic and chaotic discharges. When C4 = 0.9, switching between different periodic states is possible. Figure 7Figures 8(a)-(b) show the MATAB numerical simulation results under these conditions, corresponding to the bifurcation diagram of system x with respect to φ(0) and the time series diagram of x. Figure 7 It can be observed that φ(0) = 0.44 is the critical point for the periodic-periodic discharge transition.

[0018] The beneficial effects of this invention are as follows:

[0019] (1) The present invention provides a memristor-coupled discrete neuron system with controllable discharge mode. The introduction of a magnetically controlled memristor into the discrete neuron Rulkov system exhibits rich discharge behavior of discrete neurons, providing new ideas for the fields of neurodynamics, intelligent control, and bionics. At the same time, it provides theoretical support for the potential application of memristor-coupled discrete neurons and promotes the development of nonlinear dynamics based on memristor-coupled discrete neurons.

[0020] (2) The memristor-coupled discrete neuron system with controllable firing mode of the present invention can obtain complex firing modes by adjusting the corresponding system parameters, and can be used as a method to guide biological neuron experiments. Attached Figure Description

[0021] Figure 1 This is a module diagram of a memristor-coupled discrete neuron system with controllable firing modes simulated in MATLAB software Simulink.

[0022] Figures 2(a)-(d) show the dynamic characteristics of the system with respect to the coupling coefficient k under different initial values. Figures 2(a)-(b) show the Lyapukov exponent and bifurcation diagrams for the initial values ​​(0.1, 0.1, 0.1), and Figures 2(c)-(d) show the Lyapukov exponent and bifurcation diagrams for the initial values ​​(0.1, -2.75, -2).

[0023] Figure 3(a) shows the transient chaotic discharge diagram with initial values ​​(0.1, -2.75, 0.1), and Figure 3(b) shows the transient periodic discharge diagram with initial values ​​(0.1, -2.65, 1).

[0024] Figures 4(a)-(b) show the intermittent chaotic discharge diagrams with initial values ​​of (0.1, -2.75, 0.1) and (0.1, -2.75, 0.1), respectively.

[0025] Figure 5 The bifurcation diagram of the periodic-chaotic discharge transition with initial values ​​(0.1, -2.75, 0.1) when the system parameter k = 0.5 is given.

[0026] Figures 6(a)-(b) show the timing diagrams of x with initial values ​​of (0.1,-2.75,0.1) and (0.1,-2.75,1) respectively when the system parameter k = 0.5.

[0027] Figure 7 The bifurcation diagram of the periodic-period discharge transition with system parameter k = 0.9 and initial values ​​(0.1, -2.75, 0.1).

[0028] Figures 8(a)-(b) show the timing diagrams of x with initial values ​​of (0.1,-2.75,0.1) and (0.1,-2.75,1) respectively when the system parameter k = 0.9. Detailed Implementation

[0029] The present invention will now be described in further detail with reference to the accompanying drawings and preferred embodiments. See also: Figure 1 —Figure 8.

[0030] like Figure 1 The present invention proposes a memristor-coupled discrete neuron system with controllable firing mode, comprising three delayers U1, U2, U3, an invariant parameter C2, variable parameters C1, C3, C4, C5, C6, a hyperbolic tangent module T, a squaring module S, multipliers M1, M2, M3, a divider D, adders A1, A2, A3, A4, A5, and three outputs X, Y, Z.

[0031] The system described in this invention is simulated using Simulink, and the specific connection method is as follows:

[0032] Figure 1The second terminal of the delay unit U1 is connected to the first terminal of the squaring module S, the third terminal of the multiplier M1, the "+" terminal of the adder A2, and the first terminal of the multiplier M3; the variable parameter C3 is connected to the second terminal of the multiplier M3, and the third terminal of the multiplier M3 is connected to the first "+" terminal of the adder A5; the second terminal of the squaring module S is connected to the second "+" terminal of the adder A1, the invariant parameter C2 is connected to the first "+" terminal of the adder A1, the third terminal of the adder A1 is connected to the "÷" terminal of the divider D, the variable parameter C1 is connected to the "×" terminal of the divider D, and the third terminal of the divider D is connected to the first "+" terminal of the adder A3; the variable parameter C4 is connected to the first terminal of the multiplier M1, and the second terminal of the hyperbolic tangent module T is connected to the second terminal of the multiplier M1. The hyperbolic tangent module T is connected to the second "+" terminal of adder A5 and the second terminal of delay unit U3. The fourth terminal of multiplier M1 is connected to the second "+" terminal of adder A3. The variable parameter C5 is connected to the "-" terminal of adder A2. The third terminal of adder A2 is connected to the second terminal of multiplier M2. The variable parameter C6 is connected to the first terminal of multiplier M2. The third terminal of multiplier M2 is connected to the "-" terminal of adder A4. The second terminal of delay unit U2 is connected to the "+" terminal of adder A4 and the third "+" terminal of adder A3. The fourth terminal of adder A3 is connected to the first terminal of delay unit U1. The third terminal of adder A4 is connected to the first terminal of delay unit U2. The third terminal of adder A5 is connected to the first terminal of delay unit U3.

[0033] The model of the magnetically controlled memristor used in this invention is as follows:

[0034]

[0035] In the formula, W(φ(n)) is the memconductance, i and v are the DC current and DC voltage, respectively, f(φ(n)) is the internal state function of the memristor, and α, β, and γ are the memristor parameters;

[0036] The memristor described above is coupled to the Rulkov neuron.

[0037]

[0038] Where a, μ, and σ are Rulkov neuron parameters, 0 < μ < < 1, x(n) is the membrane potential energy, k is the coupling coefficient, a and σ control the neuron's firing state, and ε is the system parameter.

[0039] Numerical simulation experiments were conducted using Matlab. With system parameters α = 4.15, ε = 1, σ = -1.2, and μ = 0.00001, the corresponding Simulink simulation model parameters were: C1 = 4.15, C3 = 1, C5 = -1.2, C6 = 0.00001. When the initial values ​​U1 = 0.1, U2 = 0.1, and U3 = 0.1, the system remained in a periodic state. As shown in Figures 2(a)-(b), the bifurcation diagram and Lyapus exponent diagram of the system with respect to the coupling coefficient k show a bifurcation pattern of periodic and reverse-period-doubling bifurcation paths. Simultaneously, the Lyapus exponents λ1, λ2, and λ3 are all less than 0, further indicating a periodic state. When the initial values ​​were changed to U1 = 0.1, U2 = -2.75, and U3 = -2, the system exhibited a state of coexistence of periodic and chaotic discharges. As shown in Figures 2(c)-(d), the bifurcation diagram and Lyapu index diagram of the corresponding system with respect to the coupling coefficient k can be observed to show that the bifurcation diagram is a bifurcation pattern of periodic, chaotic, period-doubling bifurcation and reverse period-doubling bifurcation path. The corresponding Lyapu index is greater than 0 when it is chaotic and less than or equal to 0 when it is periodic. Obviously, chaos and periodicity coexist.

[0040] Numerical simulation experiments were conducted using Matlab. With system parameters α = 4.5, ε = 1, k = 0.5, σ = -1.2, and μ = 0.0001, the corresponding Simulink simulation model parameters were: C1 = 4.5, C3 = 1, C4 = 0.5, C5 = -1.2, and C6 = 0.0001. When the initial values ​​were U1 = 0.1, U2 = -2.75, and U3 = 0.1, the system was in a transient chaotic discharge state. As shown in Figure 3(a), the local time series diagram of system x shows that after a brief period of chaos, the time series diagram enters a four-cycle state. When the initial values ​​were U1 = 0.1, U2 = -2.65, and U3 = 1, the system was in a transient periodic discharge state. As shown in Figure 3(b), the local time series diagram of system x shows that after a brief period of three cycles, the time series diagram enters a chaotic state.

[0041] Numerical simulation experiments were conducted using Matlab. When the system parameters were selected as α = 4.5, ε = 1, k = 0.7, σ = -1.2, and μ = 0.001, the corresponding Simulink simulation model parameters were: C1 = 4.5, C3 = 1, C4 = 0.7, C5 = -1.2, and C6 = 0.001. When the initial values ​​were U1 = 0.1, U2 = -2.85, U3 = 0.1 or U1 = 0.1, U2 = -2.75, U3 = 0.1, the system was in an intermittent chaotic discharge state. As shown in Figures 4(a)-(b), the time series diagrams corresponding to system x show that the time series diagrams are chaotic and periodically alternating, and the time series diagrams are not completely the same for different initial values.

[0042] Numerical simulation experiments were conducted using Matlab. With system parameters selected as α = 4.15, ε = 1, σ = -1.2, and μ = 0.00001, the corresponding Simulink simulation model parameters were: C1 = 4.15, C3 = 1, C5 = -1.2, C6 = 0.00001. Initial values ​​were set as U1 = 0.1, U2 = -2.75, and U3 = 0.1. When C4 = 0.5, transitions between periodic and chaotic states could be performed. Figure 5 The bifurcation diagram shown indicates that φ(0) = 0.7 is the critical point for the periodic-chaotic transition. Figures 6(a)-(b) show the local time series diagrams of x from both sides of the critical value; the left side of the critical value represents a four-periodic state, and the right side represents a chaotic state. When C4 = 0.9, transitions between different periodic states are possible. Figure 7 And as shown in Figures 8(a)-(b), the bifurcation diagram of the corresponding system x with respect to φ(0) and the local timing diagram of x are shown. Figure 7 It can be observed that φ(0) = 0.44 is the critical point of the period-to-period transition. Figures 8(a)-(b) show the local time series diagrams of x from both sides of the critical value. Obviously, the two are different periodic states.

[0043] This invention presents a memristor-coupled discrete neuron system with controllable firing modes, providing new insights into the development of discrete neurons in fields such as neurodynamics, intelligent control, and bionics, and promoting the development of nonlinear dynamics in the direction of memristor-coupled discrete neurons. Furthermore, the system generates complex neuronal firing phenomena, which can be used as a special experimental method for biological neurons.

[0044] The above-disclosed embodiments are merely a few preferred embodiments of the present invention and are not intended to limit the specific implementation. Therefore, any modifications or improvements made by those skilled in the art based on the present invention should fall within the scope of protection of the present invention.

Claims

1. A discharge mode controllable memristive coupled discrete neuron system, comprising three delay units U1, U2, U3, an invariable parameter C2, variable parameters C1, C3, C4, C5, C6, a hyperbolic tangent module T, a square module S, multipliers M1, M2, M3, a divider D, and adders A1, A2, A3, A4, A5, three outputs X, Y, Z; the second end of the delay unit U1 is connected with the first end of the square module S, the third end of the multiplier M1, the "+" end of the adder A2, and the first end of the multiplier M3; the variable parameter C3 is connected with the second end of the multiplier M3, the third end of the multiplier M3 is connected with the first "+" end of the adder A5; the second end of the square module S is connected with the second "+" end of the adder A1, the invariable parameter C2 is connected with the first "+" end of the adder A1, the third end of the adder A1 is connected with the "÷" end of the divider D, the variable parameter C1 is connected with the "×" end of the divider D, the third end of the divider D is connected with the first "+" end of the adder A3; the variable parameter C4 is connected with the first end of the multiplier M1, the second end of the hyperbolic tangent module T is connected with the second end of the multiplier M1, the first end of the hyperbolic tangent module T is connected with the second "+" end of the adder A5 and the second end of the delay unit U3, the fourth end of the multiplier M1 is connected with the second "+" end of the adder A3; the variable parameter C5 is connected with the "-" end of the adder A2, the third end of the adder A2 is connected with the second end of the multiplier M2; the variable parameter C6 is connected with the first end of the multiplier M2, the third end of the multiplier M2 is connected with the "-" end of the adder A4; the second end of the delay unit U2 is connected with the "+" end of the adder A4 and the third "+" end of the adder A3; the fourth end of the adder A3 is connected with the first end of the delay unit U1, the third end of the adder A4 is connected with the first end of the delay unit U2, and the third end of the adder A5 is connected with the first end of the delay unit U3; The magnetically controlled discrete memristor is described by the following equation where W(φ(n)) is the memductance, i and v are the direct current and direct voltage respectively, f(φ(n)) is the internal state function of the memristor, and α, β, γ are the parameters of the memristor; The above magnetically controlled memristor is coupled with the Rulkov neuron wherein a, μ, σ are the parameters of the Rulkov neuron, 0 < μ << 1, x(n) is the membrane potential potential, k is the coupling coefficient, a and σ control the discharge state of the neuron, and ε is the system parameter.

2. The system of claim 1, wherein the system is a system of discharge mode controllable memristive coupled discrete neurons. The system parameter is relatively fixed, and only the initial value needs to be changed, so that the system can obtain different discharge modes, i.e. periodic discharge or coexistence of periodic and chaotic discharge modes. The corresponding simulink simulation model parameters are: C1=4.15, C3=1, C5=-1.2, C6=0.00001, when the initial value U1=0.1, U2=0.1, U3=0.1, the system is always in a periodic state; when the initial value U1=0.1, U2=-2.75, U3=-2, the system is in a periodic and chaotic coexistence state.

3. The system of claim 1, wherein the system is a system of discharge mode controllable memristive coupled discrete neurons. The system parameters are relatively fixed, and when the initial value is changed, the system will have different transient discharge phenomena; The corresponding simulink simulation model parameters are: C1=4.5, C3=1, C4=0.5, C5=-1.2, C6=0.0001, when the initial value is U1=0.1, U2=-2.75, U3=0.1, the system is in a transient chaotic state; when the initial value U1=0.1, U2=-2.65, U3=1, the system is in a transient periodic state.

4. The system of claim 1, wherein the system is a discharge mode controllable memristive coupled discrete neuron system. The system parameters are relatively fixed, and the system will have intermittent chaotic phenomena, and when the initial value is different, the intermittent chaotic state of the system is different; The corresponding simulink simulation model parameters are: C1=4.5, C3=1, C4=0.7, C5=-1.2, C6=0.001, when the initial value is U1=0.1, U2=-2.85, U3=0.1, the system is in an intermittent chaotic state; when the initial value is changed to U1=0.1, U2=-2.75, U3=0.1, the system has different intermittent chaotic phenomena.

5. The discharge mode controllable memristive coupled discrete neuron system of claim 1, wherein: The system parameters are relatively fixed, and only by changing the coupling coefficient, the discharge mode of the system can be controlled, including the transition between different periodic discharge modes and the transition between periodic discharge and chaotic discharge modes, and different coupling coefficients have different critical values when transitioning; The corresponding simulink simulation model parameters are: C1=4.15, C3=1, C5=-1.2, C6=0.00001, when the initial value is U1=0.1, U2=-2.75, U3=0.1, when C4=0.5, the system can transition between periodic and chaotic discharge; when C4=0.9, the system can transition between different periodic states.

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