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  • 标题:Stability and Hopf bifurcation analysis of fractional-order complex-valued neural networks with time delays
  • 本地全文:下载
  • 作者:R Rakkiyappan ; K Udhayakumar ; G Velmurugan
  • 期刊名称:Advances in Difference Equations
  • 印刷版ISSN:1687-1839
  • 电子版ISSN:1687-1847
  • 出版年度:2017
  • 卷号:2017
  • 期号:1
  • 页码:225
  • DOI:10.1186/s13662-017-1266-3
  • 语种:English
  • 出版社:Hindawi Publishing Corporation
  • 摘要:This paper considers a class of fractional-order complex-valued Hopfield neural networks (CVHNNs) with time delay for analyzing the dynamic behaviors such as local asymptotic stability and Hopf bifurcation. In the case of a neural network with hub and ring structure, the stability of the equilibrium state is investigated by analyzing the eigenvalue of the corresponding characteristic matrix for the hub and ring structured fractional-order time delay models using a Laplace transformation for the Caputo-fractional derivatives. Some sufficient conditions are established to guarantee the uniqueness of the equilibrium point. In addition, conditions for the occurrence of a Hopf bifurcation are also presented. Finally, numerical examples are given to demonstrate the effectiveness of the derived results.
  • 关键词:Hopfield neural networks ; fractional-order ; time delays ; hub structure ; ring structure ; stability ; Hopf bifurcation
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