Almost periodic dynamics of the delayed complex-valued recurrent neural networks with discontinuous activation functions

  • Mingming Yan
  • Jianlong Qiu
  • Xiangyong Chen
  • Xiao Chen
  • Chengdong Yang
  • Ancai Zhang
Original Article

Abstract

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.

Keywords

Almost periodic solution Discontinuous activations Global exponential stability Complex-valued 

Notes

Acknowledgements

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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interests regarding the publication of this article.

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Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  1. 1.School of Automation and Electrical EngineeringLinyi UniversityLinyiChina
  2. 2.School of Mathematical SciencesShandong Normal UniversityJinanChina
  3. 3.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia
  4. 4.School of InformaticsLinyi UniversityLinyiChina
  5. 5.Department of Electrical and Computer EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia

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