We establish an analytic local Hopf bifurcation theorem and a topological global Hopf bifurcation theorem to detect the existence and to describe the spatial-temporal pattern, the asymptotic form and the global continuation of bifurcations of periodic wave solutions for functional differential equations in the presence of symmetry. We apply these general results to obtain the coexistence of mul...

In this paper, the exponential stability problems are addressed for a class of delayed Cohen-Grossberg neural networks which are also perturbed by some stochastic noises. By employing the Lyapunov method, stochastic analysis and some inequality techniques, sufficient conditions are acquired for checking the pth(p > 1) and the 1st moment exponential stability of the network. Finally, One example...

In this paper, the problem of dynamics analysis for a class of new impulsive stochastic Cohen–Grossberg neural networks with Markovian jumping and mixed time delays is researched. Some criteria for the asymptotical stability in mean square are obtained based on linear matrix inequality (LMI) forms, which can be easily solved by LMI Toolbox in Matlab. An example is given to show the effectivenes...

In this paper, the global asymptotic stability is studied for a class of Cohen-Grossberg neural networks with time-varying and distributed delays. By employing nonlinear measure and linear matrix inequality (LMI) techniques, some new sufficient conditions are obtained to ensure the existence, uniqueness of the equilibrium point and its stability for CGNNs, where the activation functions need on...

Abstract: In this paper, the mean square exponential stability of the periodic solution for stochastic reactiondiffusion high-order Cohen-Grossberg-Type BAM neural networks with time delays is investigated. By constructing suitable Lyapunov function, applying Itô formula and Poincaré mapping, we give some sufficient conditions to guarantee the mean square exponential stability of the periodic s...

This paper presents new theoretical results on the global exponential stability of recurrent neural networks with bounded activation functions and bounded time-varying delays in the presence of strong external stimuli. It is shown that the Cohen-Grossberg neural network is globally exponentially stable, if the absolute value of the input vector exceeds a criterion. As special cases, the Hopfiel...

In this paper, we study the nonnegative periodic dynamics of the delayed Cohen–Grossberg neural networks with discontinuous activation functions and periodic interconnection coefficients, selfinhibitions, and external inputs. Filippov theory is utilized to study the viability, namely, the existence of the solution of the Cauchy problem. Under some conditions, the existence and the asymptotical ...

The impulsive control method is developed to stabilize a class of Cohen–Grossberg neural networks (CGNNs) with reaction–diffusion terms and Dirichlet boundary conditions. With the help of Lyapunov functionals, impulsive delay differential inequality and comparison principle, some sufficient conditions ensuring global exponential stability (GES) of equilibrium point are obtained. In particular, ...