Electron. J. Diff. Eqns., Vol. 2008(2008), No. 07, pp. 1-10.

Periodic solutions and exponential stability for shunting inhibitory cellular neural networks with continuously distributed delays

Le Van Hien, Tran Thi Loan, Duong Anh Tuan

Abstract:
In this paper, we consider a class of shunting inhibitory cellular neural networks with continuously distributed delays (SICNNs). The delays are unbounded and the activation function is not assumed to be bounded. Using the continuation theorems of coincidence degree theory, Lyapunov functional method, we obtain new sufficient conditions for the existence and local exponential stability of periodic solutions of (SICNNs). Numerical examples illustrated our results are given.

Submitted December 27, 2007. Published January 12, 2008.
Math Subject Classifications: 34C25, 34K13.
Key Words: Periodic solutions; exponential stability; unbounded delays; shunting inhibitory; cellular neural networks.

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Le Van Hien
Department of Mathematics
Hanoi National University of education
Add: 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
email: Hienlv@hnue.edu.vn
Tran Thi Loan
Department of Mathematics
Hanoi National University of education
Add: 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
email: Tranthiloan2001@yahoo.com
Duong Anh Tuan
Department of Mathematics
Hanoi National University of education
Add: 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
email: Tuanda@hnue.edu.vn

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