Abstract and Applied Analysis

Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays

Kaiyu Liu, Zhengqiu Zhang, and Liping Wang

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Abstract

We investigate first the existence of periodic solution in general Cohen-Grossberg BAM neural networks with multiple time-varying delays by means of using degree theory. Then using the existence result of periodic solution and constructing a Lyapunov functional, we discuss global exponential stability of periodic solution for the above neural networks. Our result on global exponential stability of periodic solution is different from the existing results. In our result, the hypothesis for monotonicity ineqiality conditions in the works of Xia (2010) Chen and Cao (2007) on the behaved functions is removed and the assumption for boundedness in the works of Zhang et al. (2011) and Li et al. (2009) is also removed. We just require that the behaved functions satisfy sign conditions and activation functions are globally Lipschitz continuous.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 805846, 21 pages.

Dates
First available in Project Euclid: 1 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364846459

Digital Object Identifier
doi:10.1155/2012/805846

Mathematical Reviews number (MathSciNet)
MR2922941

Zentralblatt MATH identifier
1242.93102

Citation

Liu, Kaiyu; Zhang, Zhengqiu; Wang, Liping. Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 805846, 21 pages. doi:10.1155/2012/805846. https://projecteuclid.org/euclid.aaa/1364846459


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