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Abstract: In this paper, we consider the following Kirchhoff-type variational inclusion system with , where and is a locally Lipschitz function and are the partial generalized gradients in the sense of Clarke. Under proper growth conditions on the nonlinearity F, the existence of nontrivial solutions for the above system is established. Our approach is variational based on the theories of nonsmooth analysis. [Copyright &y& Elsevier]

Abstract: In this paper, a delayed multispecies ecological competition-predator system with Holling-III functional response is studied. By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functionals, some sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic solutions to the system. [ABSTRACT FROM AUTHOR]

Abstract: Considered is a system of delay differential equations modeling a time-delayed connecting network of three neurons without self-feedback. Discussing the change of the number of eigenvalues with zero real part, we locate the boundary of the stability region and finally determine the largest stability region of trivial solution. We investigate the existence of bifurcation phenomena of codimension one/two of the trivial equilibrium by considering the intersections of some parameter curves, which, in the aτ-half parameter plane, correspond to zero root or pure imaginary roots. In particular, the equivariant bifurcation is studied because of the equivariance of the system. We also present numerical simulations to demonstrate the rich dynamical behavior near the equivariant Pitchfork–Hopf bifurcation points, Hopf–Hopf bifurcation points, and some higher codimension bifurcation points. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the robust control problem for a class of uncertain time-varying delayed neural networks, in which the activation function may be a discontinuous function. A robust decentralized adaptive sliding mode controller is proposed to guarantee the asymptotically stability of the system. The proposed controller, which does not dependent on the time delay, ensures the occurrence of the sliding manifold even when the system is undergoing parameter uncertainties and nonlinear input. Two numerical examples are given to show the effectiveness of the proposed controller. [Copyright &y& Elsevier]

Abstract: Without assuming that the neuron activations are bounded, some delay-independent criteria for interval delayed neural networks with discontinuous neuron activations are derived to guarantee global robust stability by using the generalized Lyapunov method and linear matrix inequality (LMI) technique. The obtained results improve and extend those given in earlier literature, and two numerical examples are also given to show the effectiveness of our results. [Copyright &y& Elsevier]

Abstract: We consider a four-neuron ring with self-feedback and delays. By analyzing the associated characteristic equation, linear stability is investigated and Hopf bifurcations are demonstrated, as well as the stability and direction of the Hopf bifurcation are determined by employing the normal form method and the center manifold reduction. Numerical simulations are presented to illustrate the results. [Copyright &y& Elsevier]

• A general Filippov-type predator-prey model with a refuge is proposed. • A The necessary and sufficient conditions for the global asymptotical stability of a standard cycle, a touching cycle and a sliding cycle are present. • The sliding cycle is proved to be globally finite-time stable. • Several kinds of sliding bifurcations are investigated. In this paper, a general Filippov-type predator-prey model with a refuge is presented. We propose a discontinuous predator-prey model incorporating a threshold policy by extending a general continuous predator-prey model. By employing the qualitative analysis theory related to Filippov systems, the necessary and sufficient conditions for the global asymptotical stability of a standard cycle, a touching cycle and a sliding cycle are obtained respectively. Furthermore, the sliding cycle is globally finite-time stable. Especially, several kinds of sliding bifurcations including boundary node bifurcation, boundary focus bifurcation and grazing bifurcation are studied. Moreover, two specific models are provided to verify the main results obtained from the general model. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider a tri-neuron network model with discrete and distributed delays. After discussing the distributions of the roots of the characteristic equation local stability analysis of the steady-state solution leads to, we analyze the stability of network models with instantaneous feedback and neural interaction history, delayed neural feedback and no neural interaction history and delayed neural feedback and neural interaction history; we give sufficient conditions for the linear stability of the equilibrium solution; we also show that a Hopf bifurcation can occur when the delays take certain critical values; and we further prove that there is a positive integer K such that there are K switches from stability to instability and back to stability. Numerical simulations are finally performed to illustrate the obtained results. [Copyright &y& Elsevier]

This paper is concerned with a class of discrete-time systems as a model for two neurons with no internal decay. Such a discrete-time system can be regarded as the discrete analog of a differential equation with piecewise constant nonlinearity of McCulloch–Pitts type. Base on some simple geometric facts, we show that all solutions of this discrete-time system are eventually periodic. [Copyright &y& Elsevier]

This paper is concerned with a delay differential system with piecewise constant nonlinearity. Such a differential system can be regarded as a model of two-neuron artificial neural network with delayed feedback. Some interesting results are obtained for the convergence and periodicity of solutions of the system. [Copyright &y& Elsevier]

In this paper, we present two types of matrix stability: complete stability and strong stability, and some properties of them. By using these properties, we discuss stability of cellular neural networks and obtain some conditions ensuring uniqueness, exponential stability and global asymptotic stability of the equilibrium point for cellular neural networks. In particular, in the two-cell case, the network is globally exponentially stable if and only if the feedback matrix minus the unit matrix is a complete stable matrix. [Copyright &y& Elsevier]

By using the Banach fixed point theorem and constructing suitable Lyapunov function, some sufficient conditions are obtained ensuring existence, uniqueness and global stability of almost periodic solution of the BAM neural networks with variable coefficients and delays. These results are helpful to design global exponential stable BAM networks and almost periodic oscillatory BAM networks. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the convergence dynamics of Cohen–Grossberg neural networks (CGNNs) with continuously distributed delays. Without assuming the differentiability and monotonicity of activation functions, the differentiability of amplification functions and the symmetry of synaptic interconnection weights, we construct suitable Lyapunov functionals and employ inequality technique to establish some sufficient conditions ensuring existence, uniqueness, global asymptotic stability, global exponential convergence, and even global exponential stability of equilibria. Our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria and can be applied to neural networks including Hopfield neural networks, bidirectional association memory neural networks and cellular neural networks. [Copyright &y& Elsevier]