Synchronization Analysis of a Class of Neural Networks with Multiple Time Delays

In this paper, we study the synchronization of a new fractional-order neural network with multiple delays. Based on the control theory of linear systems with multiple delays, we get the controller to analyse the synchronization of the system. In addition, a suitable Lyapunov function is constructed by using the theory of delay differential inequality, and some criteria ensuring the synchronization of delay fractional neural networks with Caputo derivatives are obtained. Finally, the accuracy of the method is verified by a numerical example.

Attracting and Quasi-Invariant Sets of Cohen-Grossberg Neural Networks with Time Delay in the Leakage Term under Impulsive Perturbations

A class of impulsive Cohen-Grossberg neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, the attracting and invariant sets of the networks are obtained. The results in this paper extend and improve the earlier publications. An example is presented to illustrate the effectiveness of our conclusion.

Global Exponential Robust Stability of Static Interval Neural Networks with Time Delay in the Leakage Term

The stability of a class of static interval neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, we obtain some sufficient conditions ensuring the global exponential robust stability of the networks. The results in this paper extend the corresponding conclusions without leakage delay. An example is given to illustrate the effectiveness of the obtained results.

Stability Analysis of Impulsive Stochastic Functional Differential Equations with Delayed Impulses via Comparison Principle and Impulsive Delay Differential Inequality

The problem of stability for nonlinear impulsive stochastic functional differential equations with delayed impulses is addressed in this paper. Based on the comparison principle and an impulsive delay differential inequality, some exponential stability and asymptotical stability criteria are derived, which show that the system will be stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous stochastic flows. The obtained results complement ones from some recent works. Two examples are discussed to illustrate the effectiveness and advantages of our results.

Stability of the Stochastic Reaction-Diffusion Neural Network with Time-Varying Delays andp-Laplacian

The main aim of this paper is to discuss moment exponential stability for a stochastic reaction-diffusion neural network with time-varying delays andp-Laplacian. Using the Itô formula, a delay differential inequality and the characteristics of the neural network, the algebraic conditions for the moment exponential stability of the nonconstant equilibrium solution are derived. An example is also given for illustration.

Impulsive and Diffusive Effects on Stability of BAM Neural Networks with Delays

Although the results on exponential stability of delayed bidirectional associative memory (BAM) neural networks with impulse or diffusion were reported by some researchers, impulsive and diffusive effects should simultaneously be taken account into consideration since diffusion and impulses are ubiquitous in both nature and manmade systems, which reflects a more realistic dynamics than the former results. By using the impulsive delay differential inequality, some new sufficient criteria on exponential stability are established. Our criteria are independent of diffusion effects and dependent on the magnitude of the delays and impulses, which shows that diffusion effects are harmless and the magnitude of the delays and impulses needs enough small in the stabilization.