Nonnegative Periodic Dynamics of Cohen-Grossberg Neural Networks with Discontinuous Activations and Discrete Time Delays

Authors:
Xiangnan He;Wenlian Lu;Tianping Chen
Affiliations:
Key Laboratory of Nonlinear Science of Chinese Ministry of Education, School of Mathematical Sciences, Fudan University, Shanghai, P.R. China 200433;Key Laboratory of Nonlinear Science of Chinese Ministry of Education, School of Mathematical Sciences, Fudan University, Shanghai, P.R. China 200433;Key Laboratory of Nonlinear Science of Chinese Ministry of Education, School of Mathematical Sciences, Fudan University, Shanghai, P.R. China 200433
Venue:
ISNN '09 Proceedings of the 6th International Symposium on Neural Networks on Advances in Neural Networks
Year:
2009

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Abstract

In this paper, we report the results concerned with the nonnegative periodic dynamics of the delayed Cohen-Grossberg neural networks with discontinuous activation functions and periodic interconnection coefficients, self-inhibitions, and external inputs. Filippov theory is utilized to study the viability, namely, the existence of the solution of the Cauchy problem. The conditions of diagonal dominant type are presented to guarantee the existence and the asymptotical stability of a periodic solution. Numerical examples are provided to illustrate the theoretical results.