Pinning synchronization of coupled inertial delayed neural networks

Stability and synchronization for complex-valued neural networks with stochastic parameters and mixed time delays

In this paper, a class of complex-valued neural networks (CVNNs) with stochastic parameters and mixed time delays are proposed. The random fluctuation of system parameters is considered in order to describe the implementation of CVNNs more practically. Mixed time delays including distributed delays and time-varying delays are also taken into account in order to reflect the influence of network loads and communication constraints. Firstly, the stability problem is investigated for the CVNNs. In virtue of Lyapunov stability theory, a sufficient condition is deduced to ensure that CVNNs are asymptotically stable in the mean square. Then, for an array of coupled identical CVNNs with stochastic parameters and mixed time delays, synchronization issue is investigated. A set of matrix inequalities are obtained by using Lyapunov stability theory and Kronecker product and if these matrix inequalities are feasible, the addressed CVNNs are synchronized. Finally, the effectiveness of the obtained theoretical results is demonstrated by two numerical examples.

Anti-Synchronization of Delayed State-Based Switched Inertial Neural Networks

In this article, global anti-synchronization control for a class of state-based switched inertial neural networks (SBSINNs) with time-varying delays is considered. Based on the hybrid control strategies and Lyapunov stability theory, several criteria are obtained to ensure global anti-synchronization of the underlying SBSINNs. Furthermore, we consider the global asymptotic anti-synchronization directly from the SBSINNs themselves with a nonreduced-order method. Finally, a numerical simulation is given to illustrate the effectiveness of the results.

Global exponential stabilization and lag synchronization control of inertial neural networks with time delays

The global exponential stabilization and lag synchronization control of delayed inertial neural networks (INNs) are investigated. By constructing nonnegative function and employing inequality techniques, several new results about exponential stabilization and exponential lag synchronization are derived via adaptive control. And the theoretical outcomes are developed directly from the INNs themselves without variable substitution. In addition, the synchronization results are also applied to image encryption and decryption. Finally, an example is presented to illustrate the validity of the derived results.

Stabilization of Second-Order Memristive Neural Networks With Mixed Time Delays via Nonreduced Order

In this brief, we investigate a class of second-order memristive neural networks (SMNNs) with mixed time-varying delays. Based on nonsmooth analysis, the Lyapunov stability theory, and adaptive control theory, several new results ensuring global stabilization of the SMNNs are obtained. In addition, compared with the reduced-order method used in the existing research studies, we consider the global stabilization directly from the SMNNs themselves without the reduced-order method. Finally, we give some numerical simulations to show the effectiveness of the results.

Novel Finite-Time Synchronization Criteria for Inertial Neural Networks With Time Delays via Integral Inequality Method

In this paper, we are concerned with the finite-time synchronization of a class of inertial neural networks with time delays. Without applying some finite-time stability theorems, which are widely applied to studying the finite-time synchronization for neural networks, by constructing two Lyapunov functions and using integral inequality method, two sufficient conditions on the finite-time synchronization for a class of inertial neural networks with time delays are derived. Considering that the method and research results of the finite-time synchronization are different from some existing works, this paper extends the works on the finite-time synchronization of neural networks.

Synchronization Analysis of Inertial Memristive Neural Networks with Time-Varying Delays

This paper investigates the global exponential synchronization and quasi-synchronization of inertial memristive neural networks with time-varying delays. By using a variable transmission, the original second-order system can be transformed into first-order differential system. Then, two types of drive-response systems of inertial memristive neural networks are studied, one is the system with parameter mismatch, the other is the system with matched parameters. By constructing Lyapunov functional and designing feedback controllers, several sufficient conditions are derived respectively for the synchronization of these two types of drive-response systems. Finally, corresponding simulation results are given to show the effectiveness of the proposed method derived in this paper.

Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays

This paper investigates the finite-time synchronization and fixed-time synchronization problems of inertial memristive neural networks with time-varying delays. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, several sufficient conditions are derived to ensure finite-time synchronization of inertial memristive neural networks. Then, for the purpose of making the setting time independent of initial condition, we consider the fixed-time synchronization. A novel criterion guaranteeing the fixed-time synchronization of inertial memristive neural networks is derived. Finally, three examples are provided to demonstrate the effectiveness of our main results.

Exponential synchronization of generalized neural networks with mixed time-varying delays and reaction-diffusion terms via aperiodically intermittent control

In this paper, the exponential synchronization problem of generalized reaction-diffusion neural networks with mixed time-varying delays is investigated concerning Dirichlet boundary conditions in terms of p-norm. Under the framework of the Lyapunov stability method, stochastic theory, and mathematical analysis, some novel synchronization criteria are derived, and an aperiodically intermittent control strategy is proposed simultaneously. Moreover, the effects of diffusion coefficients, diffusion space, and stochastic perturbations on the synchronization process are explicitly expressed under the obtained conditions. Finally, some numerical simulations are performed to illustrate the feasibility of the proposed control strategy and show different synchronization dynamics under a periodically/aperiodically intermittent control.

Stability and synchronization analysis of inertial memristive neural networks with time delays

This paper is concerned with the problem of stability and pinning synchronization of a class of inertial memristive neural networks with time delay. In contrast to general inertial neural networks, inertial memristive neural networks is applied to exhibit the synchronization and stability behaviors due to the physical properties of memristors and the differential inclusion theory. By choosing an appropriate variable transmission, the original system can be transformed into first order differential equations. Then, several sufficient conditions for the stability of inertial memristive neural networks by using matrix measure and Halanay inequality are derived. These obtained criteria are capable of reducing computational burden in the theoretical part. In addition, the evaluation is done on pinning synchronization for an array of linearly coupled inertial memristive neural networks, to derive the condition using matrix measure strategy. Finally, the two numerical simulations are presented to show the effectiveness of acquired theoretical results.

Passivity of memristor-based BAM neural networks with different memductance and uncertain delays

This paper addresses the passivity problem for a class of memristor-based bidirectional associate memory (BAM) neural networks with uncertain time-varying delays. In particular, the proposed memristive BAM neural networks is formulated with two different types of memductance functions. By constructing proper Lyapunov-Krasovskii functional and using differential inclusions theory, a new set of sufficient condition is obtained in terms of linear matrix inequalities which guarantee the passivity criteria for the considered neural networks. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theoretical results.