Linshan Wang

Existence, uniqueness and stability of mild solutions to stochastic reactiondiffusion CohenGrossberg neural networks with delays and Wiener processes

In this paper, we study delayed reactiondiffusion CohenGrossberg neural networks driven by infinite dimensional Wiener processes. Based on semigroup theory, existence and uniqueness of mild solutions are proved under global Lipschitz conditions. Then, some criteria of global exponential stability are obtained by using Lyapunov method and Halanay inequality. Finally, some interesting examples are provided to show the feasibility and usefulness of the developed results.

LMI-Based Approach for Exponential Robust Stability of High-Order Hopfield Neural Networks with Time-Varying Delays

This paper studies the problems of global exponential robust stability of high-order hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high-order neural networks are established, which are easily verifiable and have a wider adaptive.

Existence–uniqueness and stability of reaction–diffusion stochastic Hopfield neural networks with S-type distributed time delays

Abstract The aim of this paper is to develop some theories of mild solutions to reaction–diffusion stochastic Hopfield neural networks with S-type distributed time delays driven by infinite dimensional Wiener processes. First, we transform the networks with infinite time delays defined on ( − ∞ , 0 ] into those with finite time delays defined on [ − τ , 0 ] by truncation method. Then, the existence–uniqueness theorem of the networks with finite time delays is established in terms of the generalized Halanay inequality. Next, the existence of equilibrium is demonstrated with homotopy invariance theorem and topological degree theory. And the stability is considered using M-function. Finally, with the help of approximation method, the well-posedness and stability of the original networks are obtained. An interesting example shows the effectiveness of our results.

Robust Exponential Synchronization for Stochastic Delayed Neural Networks with Reaction–Diffusion Terms and Markovian Jumping Parameters

This paper investigates robust exponential synchronization for stochastic delayed neural networks with reaction–diffusion terms and Markovian jumping parameters driven by infinite dimensional Wiener processes. The novelty of this paper lives in the use of a new Lyapunov–Krasovskii functional and Poincaré inequality to present some criteria for robust exponential synchronization in terms of linear matrix inequalities (LMIs) and matrix measure under Robin boundary conditions. Finally, two numerical examples are provided to illustrate the effectiveness of the easily verifiable synchronization LMIs in MATLAB toolbox.

Adaptive synchronization of stochastic complex dynamical networks and its application

This paper investigates exponential synchronization for stochastic complex dynamical networks with reaction–diffusion terms and S-type distributed delays. Based on a generalized Halanay inequality and Poincaré inequality, adaptive control strategies for exponential synchronization are established by constructing a simple Lyapunov–Krasovskii functional candidate and utilizing the truncation method. Some numerical examples are provided to demonstrate the effectiveness of the obtained results. Finally, the proposed adaptive synchronization theoretical results are successfully applied to image encryption.

Global Exponential Robust Stability of High-Order Hopfield Neural Networks with S-Type Distributed Time Delays

By employing differential inequality technique and Lyapunov functional method, some criteria of global exponential robust stability for the high-order neural networks with S-type distributed time delays are established, which are easy to be verified with a wider adaptive scope.