Periodicity and multi-periodicity generated by impulses control in delayed Cohen-Grossberg-type neural networks with discontinuous activations.

Journal: Neural networks : the official journal of the International Neural Network Society
Published Date: Jun 15, 2021

Abstract

This paper discusses the periodicity and multi-periodicity in delayed Cohen-Grossberg-type neural networks (CGNNs) possessing impulsive effects, whose activation functions possess discontinuities and are allowed to be unbounded or nonmonotonic. Based on differential inclusion and cone expansion-compression fixed-point theory of set-valued mapping, several improved criteria are given to derive the positive solution with ω-periodicity and ω-multi-periodicity for delayed CGNNs under impulsive control. These ω-periodicity/ω-multi-periodicity orbits are produced by impulses control. The analytical method and theoretical results presented in this paper are of certain significance to the design of neural network models or circuits possessing discontinuous neuron activation and impulsive effects in periodic environment.

Authors

  • Zuowei Cai
    Department of Information Technology, Hunan Women's University, Changsha, Hunan 410002, PR China. Electronic address: caizuowei01@126.com.
  • Lihong Huang
    Department of Information Technology, Hunan Women's University, Changsha, Hunan 410002, PR China; College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China. Electronic address: lhhuang@hnu.edu.cn.
  • Zengyun Wang
  • Xianmin Pan
    School of Information Science and Engineering, Hunan Women's University, Changsha, Hunan 410002, China. Electronic address: 1060398673@qq.com.
  • Shukun Liu
    School of Information Science and Engineering, Hunan Women's University, Changsha, Hunan 410002, China.

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