Mean square exponential stability and periodic solutions of stochastic delay cellular neural networks.

*(English)*Zbl 1154.34395Summary: This paper mainely concerns the exponential stability analysis and the existence of periodic solution problems for a class of stochastic cellular neural networks with discrete delays (SDCNNs). Above all, Poincare contraction theory is utilized to derive the conditions guaranteeing the existence of periodic solutions of SDCNNs. Next, Lyapunov function, stochastic analysis theory and Young inequality approach is developed to derive some theorems which gives several sufficient conditions such that periodic solutions of SDCNNs are mean square exponential stable. These sufficient conditions only including those governing parameters of SDCNNs can be easily checked by simple algebraic methods. Finally, two examples are given to demonstrate that the proposed criteria are useful and effective.

##### MSC:

34K50 | Stochastic functional-differential equations |

34K13 | Periodic solutions to functional-differential equations |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

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\textit{J.-X. Lu} and \textit{Y. Ma}, Chaos Solitons Fractals 38, No. 5, 1323--1331 (2008; Zbl 1154.34395)

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