Multiple asymptotical ω-periodicity of fractional-order delayed neural networks under state-dependent switching.

Journal: Neural networks : the official journal of the International Neural Network Society
Published Date:

Abstract

This paper presents theoretical results on multiple asymptotical ω-periodicity of a state-dependent switching fractional-order neural network with time delays and sigmoidal activation functions. Firstly, by combining the geometrical properties of activation functions with the range of switching threshold, a partition of state space is given. Then, the conditions guaranteeing that the solutions can approach each other infinitely in each positive invariant set are derived. Furthermore, the S-asymptotical ω-periodicity and the convergence of solutions in positive invariant sets are discussed. It is worth noting that the number of attractors increases to 3 from 2 in a neural network without switching. Finally, three numerical examples are given to substantiate the theoretical results.

Authors

  • Jingxuan Ci
    College of Mathematics and Hunan Provincial Key Laboratory of Intelligent information processing and Applied Mathematics, Hunan University, Changsha, China. Electronic address: jxci@hnu.edu.cn.
  • Zhenyuan Guo
    College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China; Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong. Electronic address: zyguo@hnu.edu.cn.
  • Han Long
    College of Science, National University of Defense Technology, Changsha 410073, China. Electronic address: longhan@nudt.edu.cn.
  • Shiping Wen
  • Tingwen Huang