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The Existence of Anti-periodic Solution for a Class of Cellular Neural Networks


Affiliations
1 Department of Mathematics, Yuxi Normal University, Yuxi, Yunnan-653 100, China
 

In this paper, we use the Lyapunov function to establish new results on the existence and uniqueness of antiperiodic solutions for a class of cellular neural networks with time-varying delays and continuously distributed delays of
x1(t)=-di(t)hi(t,xi(t))+∑nj=1 aij(t)fj(xj(t-τij(t)))+∑nj=1 bij(t) ×∫∞0 Kij(s)gj(xj(t-s))ds+Ii(t),i=1,2,...,n.Moreover, we also present an example to illustrate the feasibility and effectiveness of our results.

Keywords

Cellular Neural Networks, Distributed Delays, Anti-periodic Solution, Exponential Stability, Delays
User

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  • The Existence of Anti-periodic Solution for a Class of Cellular Neural Networks

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Authors

Zhouhong Li
Department of Mathematics, Yuxi Normal University, Yuxi, Yunnan-653 100, China
Chenxi Yang
Department of Mathematics, Yuxi Normal University, Yuxi, Yunnan-653 100, China
Kaihong Zhao
Department of Mathematics, Yuxi Normal University, Yuxi, Yunnan-653 100, China

Abstract


In this paper, we use the Lyapunov function to establish new results on the existence and uniqueness of antiperiodic solutions for a class of cellular neural networks with time-varying delays and continuously distributed delays of
x1(t)=-di(t)hi(t,xi(t))+∑nj=1 aij(t)fj(xj(t-τij(t)))+∑nj=1 bij(t) ×∫∞0 Kij(s)gj(xj(t-s))ds+Ii(t),i=1,2,...,n.Moreover, we also present an example to illustrate the feasibility and effectiveness of our results.

Keywords


Cellular Neural Networks, Distributed Delays, Anti-periodic Solution, Exponential Stability, Delays

References





DOI: https://doi.org/10.17485/ijst%2F2010%2Fv3i1%2F29632