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This paper is concerned with the synchronization problem for a class of delayed chaotic neural networks with discontinuous activations. First a lemma which concerns stability in general decay rate is constructed. Based on this lemma, the general decay synchronization stability criteria of discontinuous neural networks are derived via a designed controller. The general decay synchronization is obtained by introducing a decay function and it contains exponential synchronization and polynomial synchronization as its two special cases. Finally, two examples are given to verify the effectiveness of the obtained results. HighlightsA new crucial lemma which concerns stability in general decay rate is constructed.General decay synchronization stability criteria of neural networks with discontinuous activations are derived.The general decay synchronization contains exponential and polynomial synchronization as its two special cases.Complete synchronization of the discontinuous neural networks can be achieved via the designed controller.The results of this paper are general and can be applied to continuous or discontinuous delayed nonlinear systems.

In this paper, a genetic regulatory network with two time delays is considered. Firstly, the stabilities with one delay and two delays are investigated. It is shown that the stability switches for time delays, and Hopf bifurcation may occur within certain range of the model parameters. Then, combining the normal form method and the center manifold theorem, we derive the explicit formulas which determine the direction of the bifurcation and the stability of the bifurcated periodic solutions. Finally, some numerical examples are exploited to support our results.

This paper is concerned with the problem of global asymptotical stability for a class of delayed genetic regularity networks (GRNs), where the time delays belong to given intervals and assumed to be time-varying. By choosing an appropriate and novel Lyapunov functional and utilizing M-matrix theory, we derive an M-matrix-based delay-range-dependent sufficient condition under which the class of considered GRNs has unique nonnegative equilibrium point which is globally asymptotically stable. The sufficient condition given here is to check whether a constructed constant matrix is a nonsingular M-matrix. This can be easily done, since there are more than 50 equivalent conditions of nonsingular M-matrix, and hence the stability criterion obtained in this paper is different from existing ones in the form of linear matrix inequality (LMI). Finally, several examples and their simulations are presented to show the effectiveness of the proposed approach.

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.