Electron. J. Diff. Eqns.,
Vol. 2006(2006), No. 32, pp. 1-21.
### Existence and exponential stability of
periodic solution for continuous-time and discrete-time
generalized bidirectional neural networks

Yongkun Li

**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.
Submitted February 16, 2006. Published March 16, 2006.

Math Subject Classifications: 34K13, 34K25.

Key Words: Bidirectional neural networks; global exponential stability;
periodic solution; Fredholm mapping; Lyapunov functionals;
discrete-time analogues.

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Yongkun Li
Department of Mathematics, Yunnan University
Kunming, Yunnan 650091, China |

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