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Zbl 1196.34063
Liu, Xiaoyang; Cao, Jinde; Huang, Gan
Complete periodic synchronization of delayed neural networks with discontinuous activations. (English)
[J] Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 7, 2151-2164 (2010). ISSN 0218-1274

Summary: Recently, the synchronization issue in chaotic systems has become a hot topic in nonlinear dynamics and has aroused great interest among researchers due to the theoretical significance and potential applications. In this paper, complete periodic synchronization is considered for the delayed neural networks with discontinuous activation functions. Under the framework of Filippov solution, a novel control method is presented by using differential inclusions theory, nonsmooth Lyapunov method and linear matrix inequality (LMI) approach. Based on a newly obtained necessary and sufficient condition, several criteria are derived to ensure the global asymptotical stability of the error system, and thus the response system synchronizes with the drive system. Moreover, the estimation gains are obtained. With these new and effective methods, complete synchronization is achieved. Simulation results are given to illustrate the theoretical results.

MSC 2000:: *34D06
34K09
34K35 Functional-differential equations connected with control problems
34K13 Periodic solutions of functional differential equations

Keywords: periodic synchronization; delayed neural networks; discontinuous activation functions; Filippov solution; nonsmooth analysis; differential inclusions; LMI approach

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