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Abstract This brief presents a class of delayed second-order memristive neural networks (SMNNs). By building a new Lyapunov functional and employing some inequalities technique, we derive some new criteria ensuring global exponential stability of the delayed SMNNs. Compared with other researches on dynamics of neural networks (NNs), our system is described by second-order differential equations and memristor. In addition, we discuss the SMNNs directly and the main results given here without changing the SMNNs into the first-order differential systems. Finally, simulations are given to elaborate the validity of the obtained criteria. [ABSTRACT FROM AUTHOR]

A new general hybrid neural networks with inertial term and mixed time-varying delays are proposed here by using the memristors connections. Then by building appropriate Lyapunov functionals and inequality technique, some new conditions assuring the global exponential stability of the hybrid neural networks are derived. The circuit implementation of the proposed hybrid neural networks are also presented here. In addition, the new proposed results here enrich and extend the earlier publications on neural networks. Lastly, numerical simulations show the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, based on the knowledge of memristor and recurrent neural networks (RNNs), the model of the memristor-based RNNs with discrete and distributed delays is established. By constructing proper Lyapunov functionals and using inequality technique, several sufficient conditions are given to ensure the passivity of the memristor-based RNNs with discrete and distributed delays in the sense of Filippov solutions. The passivity conditions here are presented in terms of linear matrix inequalities, which can be easily solved by using Matlab Tools. In addition, the results of this paper complement and extend the earlier publications. Finally, numerical simulations are employed to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the exponential synchronization of coupled memristor-based chaotic neural networks with both time-varying delays and general activation functions. And here, we adopt nonsmooth analysis and control theory to handle memristor-based chaotic neural networks with discontinuous right-hand side. In particular, several new criteria ensuring exponential synchronization of two memristor-based chaotic neural networks are obtained via periodically intermittent control. In addition, the new proposed results here are very easy to verify and also complement, extend the earlier publications. Numerical simulations on the chaotic systems are presented to illustrate the effectiveness of the theoretical results. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the global exponential anti-synchronization of a class of chaotic memristive neural networks with time-varying delays. The dynamic analysis here employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. And by using differential inclusions theory, the Lyapunov functional method and the inequality technique, some new sufficient conditions ensuring exponential anti-synchronization of two chaotic delayed memristive neural networks are derived. The new proposed results here are very easy to verify and they also improve the earlier publications. Finally, a numerical example is given to illustrate the effectiveness of the new scheme. [Copyright &y& Elsevier]

Abstract: The paper analyzes a general memristor-based recurrent neural networks with time-varying delays (DRNNs). The dynamic analysis in the paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov, and some new conditions concerning global exponential stability are obtained. In addition, these conditions do not require the activation functions to be differentiable, the connection weight matrices to be symmetric and the delay functions to be differentiable, our results are mild and more general. Finally, numerical simulations illustrate the effectiveness of our results. [Copyright &y& Elsevier]