Existence and exponential stability of periodic solution for continuous-time and discrete-time generalized bidirectional neural networks

Date

2006-03-16

Authors

Li, Yongkun

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

Abstract

We study the existence and global exponential stability of positive periodic solutions for a class of continuous-time generalized bidirectional neural networks with variable coefficients and delays. Discrete-time analogues of the continuous-time networks are formulated and the existence and global exponential stability of positive periodic solutions are studied using the continuation theorem of coincidence degree theory and Lyapunov functionals. It is shown that the existence and global exponential stability of positive periodic solutions of the continuous-time networks are preserved by the discrete-time analogues under some restriction on the discretization step-size. An example is given to illustrate the results obtained.

Description

Keywords

Bidirectional neural networks, Global exponential stability, Periodic solution, Fredholm mapping, Lyapunov functionals, Discrete-time analogues

Citation

Li, Y. (2006). Existence and exponential stability of periodic solution for continuous-time and discrete-time generalized bidirectional neural networks. <i>Electronic Journal of Differential Equations, 2006</i>(32), pp. 1-21.

Rights

Attribution 4.0 International

Rights Holder

This work is licensed under a Creative Commons Attribution 4.0 International License.

Rights License