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J. Korean Math. Soc. 2011; 48(4): 727-747
Printed July 1, 2011
https://doi.org/10.4134/JKMS.2011.48.4.727
Copyright © The Korean Mathematical Society.
Existence and global exponential stability of a periodic solution to discrete-time Cohen-Grossberg BAM neural networks with delays
Zhengqiu Zhang and Liping Wang
Hunan University, Hunan University
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 existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.
Keywords: periodic solutions, two-dimensional discrete-time Cohen-Grossberg BAM neural networks, global exponential stability, coincidence degree theory, Lyapunov functional
MSC numbers: 34D23, 39A13
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