# EXISTENCE AND GLOBAL EXPONENTIAL STABILITY OF A PERIODIC SOLUTION TO DISCRETE-TIME COHEN-GROSSBERG BAM NEURAL NETWORKS WITH DELAYS

• Zhang, Zhengqiu ;
• Wang, Liping
• Published : 2011.07.01
• 48 10

#### 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 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

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2. Global Asymptotic Stability of Periodic Solutions for Neutral-Type Delayed BAM Neural Networks by Combining an Abstract Theorem of k-Set Contractive Operator with LMI Method pp.1573-773X, 2018, https://doi.org/10.1007/s11063-018-9941-2
3. Global Asymptotic Stability of Periodic Solutions for Discrete Time Delayed BAM Neural Networks by Combining Coincidence Degree Theory with LMI Method pp.1573-773X, 2018, https://doi.org/10.1007/s11063-018-9909-2