Memristive Cohen-Grossberg Neural Networks Research Articles

Generalized-Type Multistability of Almost Periodic Solutions for Memristive Cohen-Grossberg Neural Networks.

This article investigates a generalized type of multistability about almost periodic solutions for memristive Cohen-Grossberg neural networks (MCGNNs). As the inevitable disturbances in biological neurons, almost periodic solutions are more common in nature than equilibrium points (EPs). They are also generalizations of EPs in mathematics. According to the concepts of almost periodic solutions and Ψ -type stability, this article presents a generalized-type multistability definition of almost periodic solutions. The results show that (K+1)n generalized stable almost periodic solutions can coexist in a MCGNN with n neurons, where K is a parameter of the activation functions. The enlarged attraction basins are also estimated based on the original state space partition method. Some comparisons and convincing simulations are given to verify the theoretical results at the end of this article.

Multi-synchronization of coupled multi-stable memristive Cohen–Grossberg neural networks with mixed time-delays

This paper investigates the multi-synchronization issue for a class of coupled multi-stable memristive Cohen–Grossberg neural networks with both additive time delays and distributed delays. First, the multi-stability of the isolated subnetwork with a general class of activation function is analyzed. By employing state-space decomposition, M-matrix and fixed point theory, some sufficient conditions are deduced to ensure that each subnetwork of the coupled networks has (r+1)n locally exponential stable equilibrium states. In the scenario where the time delays are continuously differentiable, a unique Lyapunov–Krasovskii function is established and some sufficient conditions are derived for the coupled system to achieve multi-synchronization under feedback control. Additionally, in circumstances where the time delays are immeasurable or discontinuous, a new feedback controller is constructed based on the system’s model parameters, and a delay-independent finite-time multi-synchronization criterion is proposed. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed methods.

Multistability of equilibrium points and periodic solutions for Clifford‐valued memristive Cohen–Grossberg neural networks with mixed delays

Based on the relevant theories of M‐matrix and the Lyapunov stability technique, this paper investigates the multistability of equilibrium points and periodic solutions for Clifford‐valued memristive Cohen–Grossberg neural networks. With the help of Cauchy convergence criterion, the exponential stability inequality is derived. The system has locally exponentially stable equilibrium points and periodic solutions, which greatly increases the number of solutions compared with the existing Cohen–Grossberg neural networks, where the is a Clifford‐valued and there is no limitation of linearity and monotonicity for activation functions. Furthermore, the attraction basins of stable periodic solutions are obtained, and it is proved that the basins can be enlarged. It is worth mentioning that the results can also be used to discuss the multistability of equilibrium points, periodic solutions, and almost periodic solutions for real‐valued, complex‐valued, and quaternion‐valued memristive Cohen–Grossberg neural networks. Finally, two numerical examples with simulations are taken to verify the theoretical analysis.

Global asymptotic synchronization of inertial memristive Cohen–Grossberg neural networks with proportional delays

In this article, the global asymptotic synchronization (GAS) using inertial memristive Cohen-Grossberg neural networks (IMCGNNs) with proportional delays (PDs) as drive–response systems is studied. By utilizing differential inclusion theory (DIT) and appropriate variable transformation, the studied systems can be converted to first-order differential systems. Both the feedback controller and the adaptive controller are designed, which are easy to implement in hardware. By constructing Lyapunov functionals and using mean value inequality analysis skills, two GAS criteria of the studied systems are gained, which are embodied in the form of algebraic inequalities and are easy to verify. Ultimately, the numerical examples with simulations are applied to sustain the obtained consequences.

Impulsive Memristive Cohen–Grossberg Neural Networks Modeled by Short Term Generalized Proportional Caputo Fractional Derivative and Synchronization Analysis

The synchronization problem for impulsive fractional-order Cohen–Grossberg neural networks with generalized proportional Caputo fractional derivatives with changeable lower limit at any point of impulse is studied. We consider the cases when the control input is acting continuously as well as when it is acting instantaneously at the impulsive times. We defined the global Mittag–Leffler synchronization as a generalization of exponential synchronization. We obtained some sufficient conditions for Mittag–Leffler synchronization. Our results are illustrated with examples.

Asymptotic Synchronization of Memristive Cohen-Grossberg Neural Networks with Time-Varying Delays via Event-Triggered Control Scheme.

This paper investigates the asymptotic synchronization of memristive Cohen-Grossberg neural networks (MCGNNs) with time-varying delays under event-triggered control (ETC). First, based on the designed feedback controller, some ETC conditions are provided. It is demonstrated that ETC can significantly reduce the update times of the controller and decrease the computing cost. Next, some sufficient conditions are derived to ensure the asymptotic synchronization of MCGNNs with time-varying delays under the ETC method. Finally, a numerical example is provided to verify the correctness and effectiveness of the obtained results.

Finite-time and fixed-time stabilization of inertial memristive Cohen-Grossberg neural networks via non-reduced order method

In this paper, we focus on the finite-time and fixed-time stabilization of inertial memristive Cohen-Grossberg neural networks. To cope with the effect caused by inertial (second-order) term, most of the previous literature use the variable translation to reduce the order. Different from that, by directly designing a Lyapunov functional and feedback controller, a novel non-reduced order method is proposed in this paper to solve the finite-time (fixed-time) stabilization problem of inertial memristive Cohen-Grossberg neural networks. Two kinds of time delays are considered in our network model, novel criteria are then derived for both cases. Lastly, numerical examples are given to verify the validity of the theoretical results.

New finite-time synchronization of memristive Cohen–Grossberg neural network with reaction–diffusion term based on time-varying delay

This paper focuses on the finite-time synchronization of memristive Cohen–Grossberg neural networks with time delays based on the reaction–diffusion term. Two new finite-time synchronous lemmas, Lemmas 2.3 and 2.4, have been obtained through some integration techniques. Since the proposal of Lemma 2.5 solves the $${X^\varphi }\left( {u\left( t \right) } \right) $$ problem in the denominator, and by designing two different controllers and inequality techniques, two finite-time synchronization theorems are finally obtained. Simulations are performed according to two examples to verify the validity of the results in this paper.

Quasi fixed-time synchronization of memristive Cohen-Grossberg neural networks with reaction-diffusion

This paper focuses on the quasi-fixed time synchronization of memristive Cohen-Grossberg neural networks with reaction diffusion. First, a new definition of finite/fixed-time attraction set and the concept of quasi finite/fixed-time synchronization are proposed. Then, a quasi fixed-time synchronized lemma is given and an example is used to illustrate the correctness of the lemma. At the same time, the new results given in this article are compared with the existing ones under certain conditions, and the conclusions of this paper are less conservative in remark. In addition, quasi fixed-time synchronization theorem and full synchronization theorem are derived by designing different controllers, finally two examples are given to illustrate the validity of these theorems.

Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations

Due to instability being induced easily by parameter disturbances of network systems, this paper investigates the multistability of memristive Cohen-Grossberg neural networks (MCGNNs) under stochastic parameter perturbations. It is demonstrated that stable equilibrium points of MCGNNs can be flexibly located in the odd-sequence or even-sequence regions. Some sufficient conditions are derived to ensure the exponential multistability of MCGNNs under parameter perturbations. It is found that there exist at least (w+2)l (or (w+1)l) exponentially stable equilibrium points in the odd-sequence (or the even-sequence) regions. In the paper, two numerical examples are given to verify the correctness and effectiveness of the obtained results.

Pinning Synchronization via Intermittent Control for Memristive Cohen-Grossberg Neural Networks With Mixed Delays

This paper presents the exponential synchronization for a class of memristive Cohen-Grossberg neural networks (MCGNNs) with mixed delays via a new hybrid control strategy. This new hybrid control strategy combines pinning control and periodic intermittent control. According to the feature of memristor, the memristive terms of the MCGNNs with mixed delays are normalized by a simple linear transformation. Then the designed periodic intermittent control is added to selected partial network nodes. Based on the stability theory of memristive neural networks and the exponential synchronization rule, the new synchronization conditions are given. Finally, numerical simulations are provided to show the effectiveness of the theoretical method.

Finite-time synchronization of memristive Cohen–Grossberg neural networks with time delays

This paper discusses the finite-time synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays. By using nonlinear transformation, an equivalent system is obtained from the discussed neural network. By investigating the finite-time synchronization of the alternative system, some finite-time synchronization criteria of the considered memristor-based Cohen–Grossberg neural network can be obtained. In the whole process, the error state |e(t)| are divided into two procedures: |e(t)| moving from initial value to 1, next, |e(t)| from 1 to 0. Especially, the error state variables e(t) move to 1 in a finite time, and move to 0 in a fixed time. Compared to the classical Lyapunov asymptotic convergence, the finite-time convergence of this paper is a new way to study the synchronization problems. Finally, numerical simulations are presented to display the obtained theoretical results.

Multistability of Almost Periodic Solution for Memristive Cohen-Grossberg Neural Networks With Mixed Delays.

This paper presents the multistability analysis of almost periodic state solutions for memristive Cohen-Grossberg neural networks (MCGNNs) with both distributed delay and discrete delay. The activation function of the considered MCGNNs is generalized to be nonmonotonic and nonpiecewise linear. It is shown that the MCGNNs with n -neuron have (K+1)n locally exponentially stable almost periodic solutions, where nature number K depends on the geometrical structure of the considered activation function. Compared with the previous related works, the number of almost periodic state solutions of the MCGNNs is extensively increased. The obtained conclusions in this paper are also capable of studying the multistability of equilibrium points or periodic solutions of the MCGNNs. Moreover, the enlarged attraction basins of attractors are estimated based on original partition. Some comparisons and convincing numerical examples are provided to substantiate the superiority and efficiency of obtained results.

New Results of Finite-Time Synchronization via Piecewise Control for Memristive Cohen-Grossberg Neural Networks With Time-Varying Delays

This paper presents the finite-time synchronization (FTS) via piecewise control laws for a class of memristive Cohen-Grossberg neural networks (MCGNNs) with time-varying delays. First, based on memristive neural network theory, differential inclusion theory, and stability theory, several new sufficient conditions are established to ensure the FTS stability of a class of MCGNNs with time-varying delays. Then, three control laws are designed. By comparison with a normal control law, the piecewise control law determined by finite-time control (FTC) θ(t) can shorten the settling time. Also, the piecewise control law determined by the dynamic error ∥e∥(t)II and FTC 8(t) can shorten the settling time. Finally, a numerical simulation example is provided to illustrate the effectiveness of the new methods.

Finite-Time Stabilization of Memristive Cohen-Grossberg Neural Networks with Time-Varying Delay

In this paper, the finite-time stabilization problem for memristive Cohen-Grossberg neural networks with time-varying delay is discussed. By using the novel fixed point theory of set-valued maps, we establish the existence theorem of equilibrium point. In order to realize the finite-time stabilization, two different kinds of discontinuous state feedback controllers whether including time-varying delay are designed. Based on the extended Filippov framework and two different kinds of methods whether using finite-time stability theory, some novel sufficient conditions and the upper bound of the settling time for finite-time stabilization are proposed. Finally, two numerical examples are given to demonstrate the validity of theoretical results.

Fixed-time Synchronization of Memristive Cohen-Grossberg Neural Networks with Impulsive Effects

This paper investigates the fixed-time synchronization of memristive Cohen-Grossberg neural networks with impulsive effects. Through a nonlinear transformation and Fillipov discontinuous theory, we obtain an equivalent system from the original memristive Cohen-Grossberg neural networks. By constructing a discontinuous Lyapunov function and utilizing comparison principle, a sufficient condition is achieved to guarantee the fixed-time synchronization of drive-response system with impulsive effects. Moreover, for the purpose of reducing the cost of control, an adaptive control strategy is considered. Finally, corresponding numerical simulations are carried out to show the effectiveness of the analytic results.

Synchronization analysis for fractional order memristive Cohen–Grossberg neural networks with state feedback and impulsive control

This paper studies drive response synchronization in fractional order memristive Cohen–Grossberg neural networks (FMCGNNs) with time delay. By applying the asymptotic expansion property of Mittag Leffler function and the definition of average impulsive, some sufficient conditions based on feedback control and impulsive control are established for achieving finite time synchronization and exponential synchronization of the FMCGNNs. Moreover, the selection of impulsive gain depends on the fractional order α. The upper bound of the setting time for synchronization is estimated and the precisely exponential convergence rate is obtained when two controllers are utilized. Finally, numerical simulations illustrate the correctness of the theoretical results for two different controllers.

New Results for Exponential Synchronization of Memristive Cohen–Grossberg Neural Networks with Time-Varying Delays

This paper concerns the topic of exponential synchronization for a class of memristive Cohen–Grossberg neural networks with time-varying delays by designing a suitable controller. Through a nonlinear transformation, we obtain an alternative system from the considered memristive Cohen–Grossberg neural networks. Then, by studying the exponential synchronization of the alternative system, we get some novel and effective exponential synchronization criteria for the considered memristive Cohen–Grossberg neural networks. These results generalize some previous known results and remove a few restrictions on control width and time-delays. Finally, numerical simulations are given to present the effectiveness of the theoretical results.

Global exponential stability of memristive Cohen–Grossberg neural networks with mixed delays and impulse time window

This paper addresses the problem of global exponential stability for a class of memristive Cohen–Grossberg with mixed time delays and impulsive time window. Based on the memristor theory, impulse control theory, and mathematical induction method, stability criteria for the considered memristive Cohen–Grossberg neural networks are derived by employing appropriate Lyapunov functions. Compared with existing impulse control schemes, the impulse instants are extended to some bounded time intervals, we will show that the neural networks can still be stable under reasonable assumptions. Furthermore, the conditions obtained in this paper are easy to be checked, and they can be applied to improve previous results concerning stability for memristive neural networks. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

Multistability of memristive Cohen–Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays

The problem of coexistence and dynamical behaviors of multiple equilibrium points is addressed for a class of memristive Cohen–Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays. By virtue of the fixed point theorem, nonsmooth analysis theory and other analytical tools, some sufficient conditions are established to guarantee that such n-dimensional memristive Cohen–Grossberg neural networks can have 5n equilibrium points, among which 3n equilibrium points are locally exponentially stable. It is shown that greater storage capacity can be achieved by neural networks with the non-monotonic activation functions introduced herein than the ones with Mexican-hat-type activation function. In addition, unlike most existing multistability results of neural networks with monotonic activation functions, those obtained 3n locally stable equilibrium points are located both in saturated regions and unsaturated regions. The theoretical findings are verified by an illustrative example with computer simulations.