Honghua Bin

Multistability of HNNs with almost periodic stimuli and continuously distributed delays

In this article, we investigate multistability of Hopfield neural networks (HNNs) with almost periodic stimuli and continuously distributed delays. By employing the theory of exponential dichotomy and Schauders fixed point theorem, sufficient conditions are gained for the existence of 2 N almost periodic solutions which lie in invariant regions. Meanwhile, we derive some new criteria for the networks to converge toward these 2 N almost periodic solutions and the domain of attraction is also given. The obtained results are new, general and improve corresponding results existing in previous literature.

CONVERGENCE AND PERIODICITY OF SOLUTIONS FOR A CLASS OF DIFFERENCE SYSTEMS

A class of difference systems of artificial neural network with two neurons is considered. Using iterative technique, the sufficient conditions for convergence and periodicity of solutions are obtained in several cases.

Subharmonics with Minimal Periods for Convex Discrete Hamiltonian Systems

We consider the subharmonics with minimal periods for convex discrete Hamiltonian systems. By using variational methods and dual functional, we obtain that the system has a -periodic solution for each positive integer , and solution of system has minimal period as subquadratic growth both at 0 and infinity.

Exponential stability of periodic solution to Wilson-Cowan networks with time-varying delays on time scales

We present stability analysis of delayed Wilson-Cowan networks on time scales. By applying the theory of calculus on time scales, the contraction mapping principle, and Lyapunov functional, new sufficient conditions are obtained to ensure the existence and exponential stability of periodic solution to the considered system. The obtained results are general and can be applied to discrete-time or continuous-time Wilson-Cowan networks.

Periodic Solutions of Second-Order Difference Problem with Potential Indefinite in Sign

We investigate the periodic solutions of second-order difference problem with potential indefinite in sign. We consider the compactness condition of variational functional and local linking at 0 by introducing new number . By using Morse theory, we obtain some new results concerning the existence of nontrivial periodic solution.

Estimate of Number of Periodic Solutions of Second-Order Asymptotically Linear Difference System

We investigate the number of periodic solutions of second-order asymptotically linear difference system. The main tools are Morse theory and twist number, and the discussion in this paper is divided into three cases. As the system is resonant at infinity, we use perturbation method to study the compactness condition of functional. We obtain some new results concerning the lower bounds of the nonconstant periodic solutions for discrete system.

Boundary Value Problems for Discrete Hamiltonian Systems with Forcing Terms

Two existence results are presented on boundary value problem for discrete Hamiltonian systems with forcing terms. Methods used here is based on the Saddle Point theorem and the Least action principle. Moreover, in order to apply variational methods, a new action functional is constructed which is different from the usual action functional for periodic boundary condition.

Memory Patterns Analysis for Discrete-Time Neural Networks with Periodic Coefficients and Time-Varying Transmission Delays

Some new criteria are obtained in this paper to guarantee that the N-dimensional discrete-time neural networks can have

Multiperiodicity analysis and numerical simulation of discrete-time transiently chaotic non-autonomous neural networks with time-varying delays

2^N

Synchronizing Neural Networks With Proportional Delays Based on a Class of

periodic memory patterns. Moreover, we provide the estimation of exponentially attractive basins for these memory patterns. These conditions improve and extend the existing results in the literature. Finally, numerical simulations are performed to illustrate our results.