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EXISTENCE AND GLOBAL EXPONENTIAL STABILITY OF A PERIODIC SOLUTION TO DISCRETE-TIME COHEN-GROSSBERG BAM NEURAL TWORKS

Liping Wang|Zhengqiu Zhang
대한수학회 (The Korean Mathematical Society)|2011.07|대한수학회지 (Journal of the KMS)|제48권 제4호|pp. 727-747

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키워드

periodic solutionsLyapunov functionalglobal exponential stabilitycoincidence degree theory
주제분류수학

초록

By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the exis-tence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the exis-tence and global exponential stability of periodic solution, the assump-tions in existing papers that the value of activation functions at zero is zero are removed.

Abstract

By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the exis-tence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the exis-tence and global exponential stability of periodic solution, the assump-tions in existing papers that the value of activation functions at zero is zero are removed.

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