Method for improving synchronization capability of neuron circuit by utilizing non-volatile memristor coupling

Abstract

The invention discloses a method for improving the synchronization capability of a neuron circuit by using nonvolatile memristor coupling. On the basis of an existing HR and tab-learning neuron model, a nonvolatile switchable memristor model is introduced to simulate synapses with long-term and short-term plasticity switchable, and a memristor coupling double-neuron model is established based on the synapses. Neuron synchronous control is realized by utilizing nonvolatile parameters of the memristor in a neuron coupling system for the first time, which is shown in that when the parameters of the memristor are volatile, the coupled neuron system needs relatively high coupling strength to realize synchronization, and when the parameters of the memristor are nonvolatile, the coupled neuron system needs relatively high coupling strength to realize synchronization. The coupling neuron system can realize synchronization under relatively small coupling strength.

Description

Technical field

[0001] The present invention belongs to the field of synchronization control technology in nonlinear dynamics. It utilizes the bionic characteristics of memristors as artificial synapses. By introducing the coupling effect of memristor synapses in two heterogeneous neuron models, when the memristors are switched to non-volatile, it can be used to simulate the long-term plasticity of neuronal synapses and improve the synchronization ability of neurons. Background Art

[0002] Brain neurons interact through synapses, promoting the realization of brain functions, among which synaptic plasticity plays a key role in information processing. Synaptic plasticity has the functions of adapting to the environment, learning and memory, and is usually divided into long-term plasticity and short-term plasticity. Short-term plasticity involves transient changes in synaptic efficacy, while long-term plasticity is characterized by persistent changes in synaptic strength and is considered to be the basis of memory storage in the human brain. In recent years, the application of models such as memristive Hindmarsh-Rose (HR), tabu-learning and FitzHugh-Nagumo (FHN) neurons and their synaptic models has revealed the important role of synaptic plasticity in the synchronous activity of neurons in different brain regions and the information transmission between neurons, and demonstrated various synchronization and discharge behaviors of neurons.

[0003] Memristors possess powerful nonlinear, plastic, memory, and storage properties, describing the rich functional relationships between charge and magnetic flux while possessing inherent biomimetic properties. Therefore, using memristors to simulate biological synapses in neurons can help recreate neuronal synchronization and firing activity. Non-volatility is a key characteristic of memristors, representing their unique memory storage capacity and enabling simulation of long-term neuronal plasticity. Currently, memristors have important applications in simulating neuronal synapses, synaptic plasticity, brain memory storage, synaptic weight update mechanisms, and steady-state plasticity.

[0004] Memristive synapses between neurons play a crucial role in synchronization, a key mechanism for the brain to achieve advanced functions such as perception, motor control, and memory consolidation. Currently, memristive synapses significantly influence the synchronization of memristive-coupled neural networks by considering coupling strength, memristor initial values, the form of the memristor equations, and the control of local active parameters. However, the influence of memristive synaptic plasticity on neuronal synchronization has been overlooked. Furthermore, the integrity of brain function is related to neuronal heterogeneity, so the heterogeneity caused by the differences in real neurons should also be considered.

[0005] In view of this, how to simulate the synchronization and dynamic behavior of synaptic plasticity (short-term plasticity and long-term plasticity) in heterogeneous neural networks, and to analyze and explore in detail the relationship between the synchronization and discharge activities of neurons and the memristive properties of non-volatile switchable memristors, are problems that technical personnel in this field urgently need to solve. Summary of the Invention

[0006] 1. Purpose of the Invention

[0007] To achieve the goal of improving the synchronization capability of neuron circuits by using nonvolatile memristor coupling, the following steps are mainly included:

[0008] Step 1: Consider a model construction of a class of non-volatile switchable memristors by tuning parameters

[0009] Step 2: Analyze the switchable mechanism of memristor to achieve non-volatility

[0010] Step 3: Consider a general model of coupled heterogeneous neurons based on nonvolatile switchable magnetically controlled memristors

[0011] Step 4: Construct synchronization judgment basis based on Lyapunov function stability analysis and Lipschitz law

[0012] Step 5: Consider two heterogeneous neuron coupling models based on non-volatile switchable magnetic memristors and verify them from the perspective of dynamic simulation

[0013] Step 6: Consider an evaluation metric for analyzing synchronization of memristor-coupled heterogeneous neurons under different memristor characteristics from the perspective of numerical simulation.

[0014] Step 7: Consider a heterogeneous neuron coupling circuit based on non-volatile switchable magnetic memristors for simulation verification

[0015] The specific process of step 1 includes: deriving a general model of the magnetically controlled memristor based on Ohm's law, i.e., the principle of the Chua memristor:

[0016]

[0017] Where V and I represent the voltage across the memristor and the current flowing through the memristor, respectively; is the memetic derivative; is the magnetic flux, Represents the first derivative of magnetic flux with respect to time; function It is related to the materials of electrical components and the corresponding physical operation mechanism. To maintain the form of the memristor function Always positive, introduce a simple quadratic term memorized form Where p and q are set to 3 and 5 respectively; consider the function Achieve non-volatile switchable, using absolute value function By realizing this memristive characteristic, the final mathematical model of the non-volatile switchable memristor is as follows:

[0018]

[0019] Where V and I represent the voltage and current flowing through the memristor, respectively; p and q are the gains that control the magnitude of the memristor current; and g and m are the memristor characteristic parameters, i.e., the modulation parameters for non-volatility. In practice, the memristor parameters can be adjusted based on actual conditions. For example, when the parameters are set to m = 1 and g = 1, the memristor model is a non-volatile memristor; when m = 1 and g = 3, the memristor model is a volatile memristor. Considering the convergence of the memristor, the parameter g must always satisfy g > 0.

[0020] Then, we analyze the switchable mechanism of memristor to achieve non-volatility in step 2. Non-volatility can be divided by the power-off graph (POP). When the number of negative slope intersections on the memristor power-off graph is greater than or equal to 2, it is non-volatile, otherwise it is volatile. Let formula (1) V = 0, and use MATLAB to clearly show and The relationship between the power outage diagram is shown in the attached figure. Figure 1 As shown in (a), when m=1, g=1, the positive slope line and the two negative slope lines are respectively The axes intersect, forming three zero points Q in POP -1 , Q0 and Q1 (i.e. When V=0 The relationship between g and memristor is shown in Figure 1, where the two intersection points are negative slopes. Therefore, the memristor exhibits non-volatility. When the g value increases to more than 2, such as when g = 3, it exhibits volatility. Figure 1 The analysis method is consistent when m is changed while g is fixed in (b).

[0021] Furthermore, considering simplifying the above analysis process, the distance L between the negative slope curve and the origin is used as the key feature of the non-volatile switching of this model. The relationship between the distance L between the zero point of the negative slope of the power-off graph and the origin can be obtained, which can intuitively reflect the non-volatility of the memristor, as shown below:

[0022]

[0023] Where L is the intersection point Q of the negative slope curve and the x-axis in the power-off diagram i (i≠0), the distance from the origin Q0 of the coordinate axis. When L=0, the memristor can be determined as a volatile memristor and can be used to simulate the short-term plasticity of neuronal synapses; when L>0, the memristor can be determined as a non-volatile memristor and can be used to simulate the long-term plasticity of neuronal synapses;

[0024] Furthermore, in step 3, a universal model of coupled heterogeneous neurons based on non-volatile switchable magnetically controlled memristors is proposed. X and Y are used to represent the internal variable set of neurons, F(X) and G(Y) are the function models of two heterogeneous neurons, and the universal model of memristors is introduced as a synapse to connect the two neurons. The connection topology of heterogeneous neurons is shown in the attached figure. Figure 2 The general mathematical model of memristive synaptic coupled heterogeneous neurons is shown as follows:

[0025]

[0026] Where X and Y are internal variables of neurons, is the state variable of the memristor; F(X) and G(Y) are two neuron function models that satisfy boundedness and differentiability; and is a function determined by the nonvolatile switchable memristor. This model will be applied to the analysis process in step 4.

[0027] Furthermore, the detailed process of step 4 includes: converting the general coupling model proposed in step 3 into an error function model, deriving the critical coupling strength satisfied by heterogeneous neuron synchronization using the Lipschitz theorem, verifying the derived results based on the stability analysis of the Lyapunov function, and roughly deriving the final critical coupling strength based on the results of numerical simulation, thus obtaining a method for improving the synchronization capability of neuron circuits by using non-volatile memristor coupling. The specific process is as follows

[0028] (1) Using the universal memristor coupled heterogeneous neuron model proposed in step 3, the error function of the model is expressed as follows:

[0029]

[0030] Where X and Y are the state variables of the two neurons, e = XY represents the synchronization error, represents the first derivative of the synchronization error function with respect to time t.

[0031] (2) Assume that the error system in equation (5) satisfies the Lipschitz condition, that is:

[0032]

[0033] Where L2 is the Lipschitz constant, and F(X)-G(X) represents the deviation of functions F and G near X. Since the simulation results show that heterogeneous neurons are asymptotically synchronized, the error can be ignored when the coupling strength is large enough. Therefore, it is concluded that a suitable Lipschitz constant L0 can always be determined to satisfy the condition ||F(X)-G(X)||≤L0||XY||. When

[0034]

[0035] This further shows that Equation (5) will satisfy the exponential rate asymptotic stability, that is, the neurons can achieve synchronization.

[0036] (3) Using the error function V(t,e)=e T The above conclusion is proved by taking e as the Lyapunov function of the error system. The derivative of this function along the error system direction can be expressed as:

[0037]

[0038] Therefore, we can get:

[0039]

[0040] Where L0 is the Lioschitz constant, which can usually be obtained by calculating the infinite norm of the Jacobian matrix (i.e. L0 = ||J|| ∞ ).when And when t→∞, the Lyapunov function satisfies V(t,e)→0. .

[0041] Furthermore, we can obtain the critical coupling strength k when neurons reach synchronization. c The relationship between and Lipschitz constant is:

[0042]

[0043] Where L0 is the Lipschitz constant. Since the Lipschitz constant L0 is determined by the internal dynamics of the neuron, it is fixed for a specific neuron.

[0044] Furthermore, due to the synchronization of memristor-coupled neurons and Function related, and the function is affected by the variable Therefore, when the coupled neurons are in a synchronous state (i.e., e=XY=0), the voltage V across the neurons will be approximately 0. The evolution process of , this process can be simplified to the analysis process of the electrocardiogram in step 2. According to the kinetic function in equation (1), The evolution process can be written as the following mathematical function:

[0045]

[0046] Furthermore, by solving equation (11), we can obtain the state variable Function conditions that are satisfied:

[0047]

[0048] The coefficients C1 and C2 depend on Since g is greater than zero, when t approaches ∞, may converge to different constant values, specifically:

[0049]

[0050] Among them, the value of C2 (-1≤C2≤1) is The initial value is directly proportional to .

[0051] Furthermore, by substituting equation (13) into equation (10), the critical synchronization value k can be derived c , and get The distance L mentioned in step 2 satisfies the following equation.

[0052]

[0053] The value of L is given by equation (2) in step 2. Since the Lipschitz constant L0 is determined only by the internal function of the neuron, it is a fixed value for a specific neuron. c While the memristor is in its volatile state, L0 remains nearly constant, and can be calculated through numerical simulation. For fixed memristor parameters (p = 3, q ​​= 5), it can be concluded that for non-volatile memristors (L ≥ 1), the required critical coupling strength will always be less than the critical coupling strength for volatile memristive synapses.

[0054] Furthermore, in step 5, considering the universality of non-volatile switchable memristors in heterogeneous neuron coupling models, the existing heterogeneous neuron model is introduced into equation (4), and the results of theoretical derivation are verified from a dynamic perspective. First, the heterogeneous tabu-tabu neuron model under mismatched memristor coupling parameters and different types of HR-tabu neuron models are introduced into step 3, and two mathematical models of heterogeneous neurons based on non-volatile switchable magnetically controlled memristors are obtained in step 4. Specifically, the first model uses the parameter w in the same tabu neuron. i As heterogeneous parameters form the heterogeneity of neurons, the second model considers replacing the second neuron in the former model with the HR neuron model to form the heterogeneity of neurons.

[0055] Taboo learning neurons are developed from Hopfield neural networks and can accurately simulate the various synchronization and discharge behaviors of neurons. i The internal functions of the tabu neurons in this case are respectively used as X, Y, i.e., F(X), G(Y) in formula (4), and the following tabu-tabu heterogeneous neuron coupling model based on memristor is obtained:

[0056]

[0057] where x 1,2 ,y 1,2 are the dimensionless state variables of neurons, and are also expressed as the membrane potential variables and internal variables of neurons; k is the coupling strength of connecting neurons, and the coupling term The quadratic electromagnetic induction effect is reflected by the α = 0.2, b = 0.3, c = 0.5, d = 1, w2 = 5.2, p = 3, q ​​= 5, and β = 1. The heterogeneity is reflected by the difference in w2.

[0058] The second-order Hindmarsh-Rose (HR) neuron model has low complexity but can accurately simulate and predict the frequency-current relationship. It is often used to simulate various synchronization and discharge behaviors of neurons. Substituting the HR neuron model into the X and F(X) corresponding to the general model in Equation (4) yields the memristor-based HR-tabu heterogeneous neuron coupling model as follows:

[0059]

[0060] Where x1 and y1 represent the membrane potential variable of HR neurons and the recovery variable related to the intracellular current of neurons, respectively. Other parameters can be fixed as a1=1, b1=3, c1=1, d1=5, a2=0.2, b2=0.3, c2=0.5, d2=1, w=5.2, p=3, q=5 and β=1.

[0061] Furthermore, in step 6, an evaluation index for analyzing the correlation of memristive coupled heterogeneous neurons under different characteristics is considered from the perspective of numerical simulation to clearly demonstrate the synchronization ability of neurons under different memristive characteristics. The results of neuron synchronization ability under different memristive characteristics are visualized and analyzed to obtain the attached Figure 3 , 4, 5, and attached Figure 6 The corresponding variables and their error time series diagram. The synchronization factor R characterizes the correlation of time series from the perspective of mean field theory and is defined as:

[0062]

[0063] Where N represents the number of sequences in the system. For the neuron coupling model proposed above, N = 2. t i and t e Indicates the start and end time of the calculation, Δt=t e -t i Obviously, the larger the value of R, the higher the correlation of the sequence. When R = 1, it means that the coupled neuron model achieves complete synchronization.

[0064] Finally, in step 7, based on Kirchhoff’s circuit laws, the circuit characteristics of the operational amplifier, and the voltage-current relationship of the circuit elements, a nonvolatile switchable memristor-coupled HR-tabu neuron equivalent circuit model is considered and simulated. The equivalent circuit equation can be derived as follows:

[0065]

[0066] Where R0=10kΩ,C i =100μF. The other parameters of the circuit can be set as: R a1 =10kΩ, R b1 =3.33kΩ, R c1 =10kΩ, R d1 =2kΩ, R a2 =50kΩ, R b2 =33.3kΩ, R c2 =20kΩ, R d2 =10kΩ, R β =20kΩ, R m =10kΩ, E=1V.

[0067] Finally, draw the circuit schematic in PSIM software as shown below: Figure 10 As shown in the figure, the physical simulation experiment can be carried out with the help of PSIM software, and compared with the MATLAB numerical solution method.

[0068] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for improving the synchronization capability of neuron circuits by coupling non-volatile memristors, which has the following beneficial effects:

[0069] 3.Beneficial effects:

[0070] The present invention proposes a method for switching a memristor between volatility and non-volatility, namely, achieving non-volatility by changing two parameters within the memristor. This is related to the switching of neuronal synaptic plasticity. At the same time, it is introduced as a coupled synapse into two different heterogeneous neuron models, and two non-volatile switchable memristor coupled heterogeneous neuron models are established. Then, from the perspective of dynamic numerical simulation, the neuronal sequence correlation under the coupling of memristors with different memristive characteristics (volatile, non-volatile) during the coupling process is analyzed. It is observed that when the memristor switches to different memristive characteristics, the neuronal sequence correlation is different. Specifically, when the coupling strength is fixed, the heterogeneous neurons under the action of non-volatile memristive synapses have better synchronization ability than those under volatile ones, which is another way to improve the synchronization ability of neurons. Finally, the mechanism of this process is analyzed and verified using the Lipschitz theorem, the stability theory of Lyapunov functions, and circuit simulation experiments. Since synaptic plasticity of neurons is closely related to long-term learning, memory and synchronization of hippocampal neurons in the human brain, these results and analysis methods will help to understand and study the neural signal transmission and processing mechanisms of heterogeneous neurons under synaptic-intervention coupling. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 Shown is the power-off diagram of the memristor and the relationship between the minimum distance L between the intersection point of the negative slope and the origin in the gm dual-parameter space domain.

[0072] Figure 2 Shown is the structure of a memristor coupled heterogeneous neuron.

[0073] Figure 3 The figure shows the coupling strength-correlation coefficient curve of tabu-tabu neurons under different memristor parameters (characteristics).

[0074] Figure 4 The diagram shows the critical coupling strength of tabu-tabu neurons under different memristor parameters (characteristics).

[0075] Figure 5 Shown is the serial correlation coefficient diagram of HR-tabu neurons under different memristor parameters (characteristics)

[0076] Figure 6 Time series diagram of neuron membrane potential variables and their errors under different memristor parameters (characteristics)

[0077] Figure 7 Shown is the correlation diagram of HR-tabu neurons under different memristor parameters (characteristics) in the dual-parameter space domain

[0078] Figure 8 Shown is the critical coupling strength diagram of HR-tabu neurons under different memristor parameters (characteristics)

[0079] Figure 9 The synchronous critical coupling strength value derived using Lipschitz theorem combined with numerical simulation

[0080] Figure 10 Nonvolatile switchable memristor coupled HR-tabu neuron circuit model

[0081] Figure 11 Simulation timing diagram of non-volatile switchable memristor coupled HR-tabu neuron circuit DETAILED DESCRIPTION

[0082] In order to make the purpose, features and advantages of the present invention more clearly understood, the following is a further detailed description with reference to the accompanying drawings and specific embodiments:

[0083] The present invention discloses a method for improving the synchronization capability of neuron circuits by coupling nonvolatile memristors, including realizing that the memristor can switch between volatility and non-volatility by using only two parameters inside the memristor; formulating the key characteristics of the non-volatility switching of the memristor in combination with the power-off diagram; and finally displaying the results in Figure 1 Specifically, when m=1, the memristor power-off diagrams formed under different parameters g are as follows: Figure 1 As shown in (a), when m=1, g=1, the positive slope line and the two negative slope lines are respectively The axes intersect, forming three zero points Q in POP -1 , Q0 and Q1 (i.e. Compared with V=0 The two points are the intersection of negative slopes, so the memristor shows non-volatility. When the g value increases beyond 2, such as g = 3, it shows volatility. Fixed g = 2 corresponds to Figure 1 (b) The analytical method and Figure 1 (a) Consistent. In general, when the parameters satisfy 2m<g(g> 0), the memristor is volatile, simulating the short-term plasticity of neuronal synapses. Otherwise, it is non-volatile, simulating the long-term plasticity of neurons. Next, the key characteristic of the change between the intersection of the negative and positive slopes, namely the distance L, is formalized. This yields a theoretical mg two-parameter plane diagram for distance L. It can be seen that the light-colored line in the middle divides the parameter space into the volatile (left) and non-volatile (right) space, respectively.

[0084] Then, the memristor is introduced into the heterogeneous neuron model to obtain the structure diagram of the non-volatile switchable memristor coupled heterogeneous neuron, see Figure 2The two neurons with different grayscales above and below represent two heterogeneous neurons, which are connected to each other through synapses. The synaptic model is shown in the enlarged ellipse between the two models. Consider introducing a memristor as an artificial synapse to realize the connection between neurons, and the coupling method is direct coupling.

[0085] The coupled general mathematical model corresponds to the following:

[0086]

[0087] Where X and Y represent the internal variable set of the neuron; F(X) and G(Y) are the function models of two heterogeneous neurons; Shown with is a direct coupling form with a memristor function and a coupling strength of k. Subsequently, the two heterogeneous neuron mathematical models are substituted into the two different memristor coupled heterogeneous neuron mathematical models, as shown in Equations (4) and (5).

[0088] In order to evaluate the synchronization between two memristor-coupled neurons, the synchronization factor R is defined based on the time series correlation of the two coupled neurons according to the mean field theory:

[0089]

[0090] Where N represents the number of sequences in the system. For the neuron coupling model proposed above, N = 2. t i and t e Indicates the start and end time of the calculation, Δt=t e -t i .

[0091] Dynamic numerical simulation and theoretical derivation:

[0092] The mathematical model of Equation (4) was solved by the Runge-Kutta method in Matlab, and the synchronization factor R under different coupling strengths k was calculated, as shown in the following example: Figure 3 The coupling strength-correlation curve is shown in Figures (a), (b), (c), and (d) set up control implementations with different parameters, corresponding to w1 = 0.9 and 1.5 respectively. The experiment used a non-volatile memristor (m = 1, g = 0.2, 0.5, 2, see Figure 3 (a); g = 2, m = 1, 3, 6, see Figure 3 (b)) and volatile memristors (m = 1, g = 3, 4, see Figure 3 (a)(c); g = 2, m = 0.1, 0.5, see Figure 3(b)(d)). The results show that the R value reaches 1 faster for non-volatile memristors, while it is slower for volatile memristors. Therefore, non-volatile memristors help achieve synchronization between non-identical neurons. When the parameter mismatch between two coupled neurons is reduced, Figure 3 (c) (d) When the parameter mismatch between the two coupled neurons decreases (w1 = 1.5, w2 = 5.2), the R value still approaches 1 faster, although in this case, the R value is more likely to exceed the case with larger parameter mismatch. From the above analysis, it can also be seen that the synchronization process of heterogeneous neurons always satisfies asymptotic synchronization.

[0093] Furthermore, in order to more accurately study the synchronization ability of heterogeneous tabu learning neurons coupled with memristors under different memristive characteristics, Figure 4 The key coupling strength k is recorded c The synchronization factor R = 0.98 ( Figure 3 dashed line in the middle). Figure 4 (a) shows the k c With the increase of g value, k c Also increases, when g is greater than 2m, k c It stabilizes at about 0.93. Since the memristor changes from non-volatile to volatile when g is greater than 2m, the synchronization capability suddenly decreases as the memristor becomes volatile. These results are verified by Figure 4 k for given parameters g = 1.0, 2.0, 3.0 and w1 = 0.9, w2 = 5.2 in (b) c The relationship with m is verified, where k is greater than g / 2 (i.e., non-volatile). c From a constant value of about 0.93 to a small value. At the same time, for the case where the neuron parameter mismatch is small (w1 = 1.5, w2 = 5.2), in addition to the critical coupling strength k c The results are similar except that the value becomes 0.26 instead of 0.93. Figure 4 (c) (f) show the critical coupling strength k when w1 = 0.9 and 1.5 when the memristor is in the nonvolatile state. c The relationship between the distance L (L>1). Obviously, as the distance L increases, the critical value k of synchronization c When the memristor is non-volatile, the synchronization is enhanced as the distance L increases.

[0094] Furthermore, we consider the synchronization effect of non-volatile memristors on another heterogeneous neuron type (HR-tabu neurons). Figure 5Figures (a) and (b) show the relationship between the synchronization factor R and the coupling strength k for different parameters g and m. When g ≤ 2m (for nonvolatile memristors, i.e., m = 1, g = 0.1, 0.5, 2), R increases toward 1 more rapidly. However, when g > 2m (for volatile memristors, i.e., m = 1, g = 3, 4), R increases toward 1 more slowly. This suggests that two different neurons can more easily achieve synchronization through nonvolatile memristor coupling.

[0095] Then, the specific differences are displayed from the time series visualization of the variables. Figure 6 (a)-(h) show the changes in membrane potential x1, x2, and synchronization error Δx(t) in the HR-tabu neural network under given coupling strengths (k = 0.5 and k = 10). The former corresponds to non-volatile memristive coupling (m = 1, g = 1), while the latter corresponds to volatile memristive coupling (m = 1, g = 3). Clearly, neurons with non-volatile memristive coupling have smaller synchronization errors.

[0096] Next, in order to more intuitively and comprehensively demonstrate the relationship between memristive characteristics and HR-tabu neural network synchronization, Figure 7 (a) (b) shows the relationship between the synchronization factor R of two coupled neurons and the parameters g and k when m = 1 (or m and k parameters when g = 2). The purple area in the figure marks the parameters with large synchronization factor R (R ≥ 0.98), which determines the critical coupling value k for synchronization under given parameters g or m. c Since the parameters m and g determine the plasticity of synapses, the synchronization of neural networks is affected by synaptic plasticity. Under the influence of non-volatile synapses, HR-tabu neural networks can achieve a higher synchronization factor R at a smaller coupling strength. In contrast, when synapses are in a volatile state, a higher coupling strength is required to achieve synchronization.

[0097] Consistent with the above, it shows that Figure 8 (a)( Figure 8 (b)) Given m = 1 (parameter m corresponds to parameter g = 2) the synchronization threshold k c The effect of the non-volatility of the memristor on synchronization is similar to that of the coupled heterogeneous tabu-tabu neurons mentioned above. c It first increases with the increase of g and then reaches a maximum value (k c =1), such as Figure 8 (a) shows that m is 0.5, 1.0, and 1.5. At the same time, when the memristor changes from the volatile state to the non-volatile state, the critical value k of synchronization cAs m increases, it shows a quadratic function trend.

[0098] Then, after deducing the synchronization judgment basis based on the stability analysis of the Lyapunov function and the Lipschitz law in step 4, the numerical simulation method was combined to obtain Figure 9 The results shown are simulation data and the solid line is theoretical data. Specifically, when m = 0.5, 1.0, 1.5 (or g = 1, 2, 3), the synchronous critical coupling strength k obtained from formula (13) is c The relationship between g and Figure 9 The numerical results in (a) and (b) are very consistent. At the same time, based on the double logarithmic coordinate axis of formula (15), the critical value k c The relationship between the distance L and Figure 9 The numerical results in (c) are also in good agreement, where the parameter w1 in f1(x) is set to 0.9 and 1.5, respectively. Obviously, the mismatch in the parameters of the two coupled neurons will affect the absolute value of the critical coupling strength for synchronization (related to L0), but will not affect the critical value k c The relationship between L.

[0099] Finally, based on Kirchhoff's circuit laws, the circuit characteristics of the operational amplifier, and the voltage-current relationship of the circuit elements, an equivalent circuit model of a nonvolatile switchable memristive-coupled HR-tabu neuron can be derived as follows:

[0100]

[0101] Where R0=10kΩ,C i =100μF. The other parameters of the circuit can be set as: Ra1 = 10kΩ, Rb1 = 3.33kΩ, R c1 =10kΩ, R d1 =2kΩ, R a2 =50kΩ, R b2 =33.3kΩ, R c2 =20kΩ, R d2 =10kΩ, R β =20kΩ, R m =10kΩ, E=1V.

[0102] According to the above mathematical model, a circuit schematic diagram of HR-tabu neuron coupled with non-volatile switchable memristor is designed, as shown in the figure. Figure 10As shown. It mainly includes: (a) HR neuron circuit model, (b) tabu learning neuron circuit model, (c) tabu learning neuron activation function circuit model, (d) non-volatile switchable memristor circuit model. The specific connection method is to use the output x2 in circuit (b) and (d) As a partial coupling term input circuit (a); with the output x1 in circuit (a) (d), As part of the coupling term input circuit (b); (c) the tabu-learning neuron activation function -f(x) is input into circuit (b); (d) the memristor equivalent circuit module is used as a coupling module, and the coupling terms are output respectively. To circuits (a) and (b).

[0103] With the help of electronic circuit simulation software PSIM, Figure 11 (a)-(h) show the dynamic characteristics of the memristor coupled neuron model and its synchronization error. These results are consistent with Figure 6 The phenomena shown in (a)-(h) are consistent. According to equations (5) and (18), g = 1 / (R g C i ), m=1 / (R m C i ), k=1 / (R k Ci). When the resistance R g Set to 10kΩ, R k Set to 20kΩ (or R k When the memristor is in a non-volatile state (corresponding to m = 1, g = 1, k = 0.5 or 10), the coupled neuron is in the R k = 20kΩ when there is no synchronization, but when R k =1kΩ, as shown in Figure 13(a)-(d). However, when the memristor is in the volatile state (corresponding to m = 1, g = 3, k = 0.5 or 10), that is, R g Set to 3.33kΩ, R k Set to 20kΩ (or R k When the coupled neuron is at R k = 20kΩ and R k = 1 kΩ, synchronization still fails, as shown in Figure 13(e)-(h). Therefore, when the coupled memristors are in a non-volatile state, the coupled neurons are more likely to synchronize.

[0104] This invention proposes a method for improving the synchronization capability of neuronal circuits by utilizing nonvolatile memristor coupling. This method dynamically improves neuronal synchronization by simulating the nonvolatile synaptic plasticity of neurons using memristors, providing another neuromorphic computing method. Compared to traditional fixed coupling methods, this method leverages the storage characteristics of memristors to significantly improve the synchronization capability of neuronal networks, providing a new technical approach for brain-inspired computing, intelligent perception, and neuromorphic hardware design. Experimental simulations and theoretical derivations demonstrate that in a typical heterogeneous neuronal network, this method indirectly improves the connection strength between neurons by simulating both long-term and short-term synaptic plasticity until synchronization is achieved, demonstrating its significant application value. This document systematically illustrates the principles and implementation methods of the invention through specific implementation methods, aiming to facilitate understanding of the core concepts of the method. Those skilled in the art may modify or substitute these specific implementation methods without departing from the overall concept of the invention. Furthermore, based on the principles of the invention, adaptive adjustments may be made to the implementation methods and scope of application. In summary, the contents of this specification should not be construed as limiting the invention.

Claims

1. A method for improving the synchronization capability of neuron circuits by using nonvolatile memristor coupling, characterized in that The following steps are involved: Step 1: Consider a model construction of a class of non-volatile switchable memristors by tuning parameters According to the memristor state equation and the related Ohm's law and Chua's theorem, a general electromagnetically controlled memristor is expressed as follows: Where V and I represent the voltage and current flowing through the memristor, respectively; is the memetic derivative; is the magnetic flux, Represents the first derivative of magnetic flux with respect to time; function The memristor parameter is related to the material of the electrical component and the corresponding physical operating mechanism; p and q are the gains that control the magnitude of the memristor current; g and m are the memristor characteristic parameters, that is, the modulation parameters of non-volatility. In reality, the memristor parameters can be adjusted according to actual conditions. For example, when the parameters are set to m = 1 and g = 1, the memristor model is a non-volatile memristor; when m = 1 and g = 3, the memristor model is a volatile memristor. Step 2: Analyze the switchable mechanism of memristor to achieve non-volatility The non-volatility of the memristor can be quickly determined through the power-off graph. The non-volatile switchable mechanism of the memristor model proposed in the first step is formalized to obtain the relationship between the distance L between the zero point of the negative slope of the power-off graph and the origin. This can intuitively reflect the non-volatility of the memristor, as shown below: Where L is the intersection point Q of the negative slope curve and the x-axis in the power-off diagram i (i≠0), the distance from the origin Q0 of the coordinate axis. When L=0, the memristor can be determined as a volatile memristor and can be used to simulate the short-term plasticity of neuronal synapses; when L>0, the memristor can be determined as a non-volatile memristor and can be used to simulate the long-term plasticity of neuronal synapses; Step 3: Consider a general model of coupled heterogeneous neurons based on nonvolatile switchable magnetically controlled memristors As shown below: Where X and Y are internal variables of neurons, is the state variable of the memristor; F(X) and G(Y) are two neuron function models that satisfy boundedness and differentiability; and is a function determined by the nonvolatile switchable memristor. This model will be applied to the analysis process in step 4. Step 4: Construct synchronization judgment basis based on Lyapunov function stability analysis and Lipschitz law For the universal memristor-coupled heterogeneous neuron model proposed in step 3, the synchronization conditions of the heterogeneous neuron coupling model can be approximately solved by combining Lyapunov function stability analysis and Lipschitz theorem with simulation data. The method flow is as follows: First, through the universal memristor-coupled heterogeneous neuron model proposed in step 3, the error function of the model is expressed as follows: Where X and Y are the state variables of the two neurons, e = XY represents the synchronization error, Represents the first derivative of the synchronization error function. Assume that the error system satisfies the Lipschitz condition, that is: Where L2 is the Lipschitz constant, and F(X)-G(X) represents the deviation of functions F and G near X. Since the two neurons and their associated error functions satisfy the conditions of boundedness and differentiability, we can establish the inequality ||F(X)-G(X)||≤C0, where the constant C0 becomes asymptotically negligible as the error approaches zero. Alternatively, when X=Y or X→Y, there is obviously an L1 such that ||F(X)-G(X)||≤L1||XY|| is always satisfied. Therefore, by integrating the above expressions, we can always determine a suitable Lipschitz constant L0 that satisfies the condition ||F(X)-G(X)||≤L0||XY||. When This shows that equation (4) will satisfy the exponential rate asymptotic stability. Next, we use the related theorem to prove this point. Using the error function V(t,e)=e T e is the Lyapunov function of the error system. The derivative along the error system direction can be expressed as: Therefore, we can get: when And when t→∞, the Lyapunov function satisfies V(t,e)→0. Where L0 is the Lioschitz constant. Then, the critical coupling strength k when neurons reach synchronization can be obtained c The relationship between and Lipschitz constant is: Where L0 is the Lipschitz constant. Since the Lipschitz constant L0 is determined by the internal dynamics of the neuron, it is fixed for a specific neuron. According to the memristor dynamics function in equation (1), when the neurons are synchronized, the voltage V across the memristor is approximately 0, which can be theoretically explained. The following mathematical function is derived from the evolution process of Then, by solving equation (10), we can get the state variable Function conditions that are satisfied: The value of C2 (-1≤C2≤1) is The initial value is directly proportional to . Finally, by substituting equation (11) into equation (9), the critical synchronization value k can be derived c , and get The distance L mentioned in step 2 satisfies the following equation. in, The value of parameter L is given by equation (2) in step 2. Since the Lipschitz constant L0 is determined only by the internal function of the neuron, it is a fixed value for a specific neuron. c When the memristor is in the volatile state, L0 remains almost constant, and can be calculated numerically. For fixed memristor parameters (p = 3, q ​​= 5), it can be concluded that the critical coupling strength required for non-volatile memristors (L ≥ 1) will always be less than the critical coupling strength under volatile memristive synapses. Step 5: Consider two heterogeneous neuron coupling models based on non-volatile switchable magnetic memristors and verify them from the perspective of dynamic simulation Consider two cases of heterogeneous neuron coupling models, namely the heterogeneity caused by mismatched neuron model parameters and different types, as shown below: Formula (4) is the parameter w coupled by the memristor i Tabu-tabu heterogeneous neuron coupling model under mismatch. 12 ,y 12 are the dimensionless state variables of neurons, k is the coupling strength of connected neurons, and the coupling term The quadratic electromagnetic induction effect is reflected by the α = 0.2, b = 0.3, c = 0.5, d = 1, w2 = 5.2, p = 3, q ​​= 5, and β = 1. The heterogeneity is reflected by the difference in w2. Equation (5) shows the heterogeneity caused by memristor coupling of different types of neurons, i.e., the mathematical model of HR-tabu neuron coupling based on memristors. Here, x1 and y1 represent the membrane potential variable of the HR neuron and the recovery variable related to the intracellular current of the neuron, respectively. Other parameters can be fixed as a1 = 1, b1 = 3, c1 = 1, d1 = 5, a2 = 0.2, b2 = 0.3, c2 = 0.5, d2 = 1, w = 5.2, p = 3, q ​​= 5, and β = 1. Step 6: Consider an evaluation metric for analyzing synchronization of memristive-coupled heterogeneous neurons under different characteristics from the perspective of numerical simulation. The synchronization factor R characterizes the correlation of time series from the perspective of mean field theory and is defined as: Where N represents the number of sequences in the system. For the neuron coupling model proposed above, N = 2. t i and t e Indicates the start and end time of the calculation, Δt=t e -t i Obviously, the larger the value of R, the higher the correlation of the sequence. When R = 1, it means that the coupled neuron model achieves complete synchronization. Step 7: Consider a heterogeneous neuron coupling circuit based on non-volatile switchable magnetic memristors for simulation verification According to Kirchhoff’s circuit law, the circuit characteristics of the operational amplifier and the voltage-current relationship of the circuit elements, a non-volatile switchable memristor coupled HR-tabu neuron equivalent circuit model is given, corresponding to equation (14). The circuit equation can be derived as follows: Where R0=10kΩ,C i =100μF. The other parameters of the circuit can be set as: Ra1 = 10kΩ, Rb1 = 3.33kΩ, R c1 =10kΩ, R d1 =2kΩ, R a2 =50kΩ, R b2 =33.3kΩ, R c2 =20kΩ, R d2 =10kΩ, R β =20kΩ, R m =10kΩ, E=1V. Finally, the schematic diagram is drawn with the help of PSIM software and physically feasible simulation experiments are carried out, which are compared and verified with the MATLAB numerical solution method. Through the above steps, a method for improving the synchronization ability of neuron circuits by using non-volatile memristor coupling is given.

Images