Open AccessExistence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays
Author(s) -
Kaiyu Liu,
Zhengqiu Zhang,
Liping Wang
Publication year - 2012
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2012/805846
Subject(s) - mathematics , exponential stability , lipschitz continuity , monotonic function , stability (learning theory) , sign (mathematics) , exponential function , exponential dichotomy , artificial neural network , control theory (sociology) , mathematical analysis , computer science , differential equation , nonlinear system , physics , control (management) , quantum mechanics , machine learning , artificial intelligence
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
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