Nonnegative periodic dynamics of delayed Cohen-Grossberg neural networks with discontinuous activations

Authors:
Xiangnan He;Wenlian Lu;Tianping Chen
Affiliations:
Shanghai Key Laboratory for Contemporary Applied Mathematics, Key Laboratory of Nonlinear Science of Chinese Ministry of Education, School of Mathematics, Fudan University, Shanghai 200433, PR Chi ...;Shanghai Key Laboratory for Contemporary Applied Mathematics, Key Laboratory of Nonlinear Science of Chinese Ministry of Education, School of Mathematics, Fudan University, Shanghai 200433, PR Chi ...;Shanghai Key Laboratory for Contemporary Applied Mathematics, Key Laboratory of Nonlinear Science of Chinese Ministry of Education, School of Mathematics, Fudan University, Shanghai 200433, PR Chi ...
Venue:
Neurocomputing
Year:
2010

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Abstract

In this paper, we study 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. Under some conditions, the existence and the asymptotical stability of a periodic solution are derived. Numerical examples are provided to illustrate the theoretical results.