Almost periodic dynamics of the delayed complex-valued recurrent neural networks with discontinuous activation functions
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The target of this article is to study almost periodic dynamical behaviors for complex-valued recurrent neural networks with discontinuous activation functions and time-varying delays. We construct an equivalent discontinuous right-hand equation by decomposing real and imaginary parts of complex-valued neural networks. Based on differential inclusions theory, diagonal dominant principle and nonsmooth analysis theory of generalized Lyapunov function method, we achieve the existence, uniqueness and global stability of almost periodic solution for the equivalent delayed differential network. In particular, we derive a series of results on the equivalent neural networks with discontinuous activation functions, constant coefficients as well as periodic coefficients, respectively. Finally, we give a numerical example to demonstrate the effectiveness and feasibility of the derived theoretical results.
KeywordsAlmost periodic solution Discontinuous activations Global exponential stability Complex-valued
This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61273012, 61403179, 61304023 and 61503171, in part by the Natural Science Foundation of Shandong Province of China under Grant Nos. ZR2014AL009, ZR2014CP008 and ZR2015FL021 and in part by the AMEP of Linyi University.
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Conflict of interest
The authors declare that they have no conflict of interests regarding the publication of this article.
- 4.Yang S, Guo Z, Wang J (2016) Global synchronization of multiple recurrent neural networks with time delays via impulsive interactions. IEEE Trans Neural Netw Learn Syst 15(2):318–328Google Scholar
- 7.Mathes JH, Howell RW (1997) Complex analysis for mathematics and engineering, 3rd edn. Jones and Bartlett Pub. Inc., BurlingtonGoogle Scholar
- 41.Li Y, Wu H (2009) Global stability analysis for periodic solution in discontinuous neural networks with nonlinear growth activations. Adv Differ Equ 2009. doi: 10.1155/2009/798685
- 48.He C (1992) Almost periodic differential equation. Higher Education Publishing House, BeijingGoogle Scholar