Hopf bifurcation and stability analysis on discrete-time Hopfield neural network with delay

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• 作者：Hongyong Zhao ; Lei Wang ; Changxiu Ma
• 关键词：Hopfield neural networks ; Discrete time ; Neimark– ; Sacker bifurcation ; Stability ; Periodic solution
• 刊名：Nonlinear Analysis ; Real World Applications
• 出版年：2008
• 期刊代码：44_14681218
• 类别：mt
• 出版时间：February 2008
• 卷：9
• 期：1
• 页码：103-113
• 文件大小：1521 K

摘要

In this paper, a discrete-time Hopfield neural network with delay is considered. We give some sufficient conditions ensuring the local stability of the equilibrium point for this model. By choosing the delay as a bifurcation parameter, we demonstrated that Neimark–Sacker bifurcation (or Hopf bifurcation for map) would occur when the delay exceeds a critical value. A formula for determining the direction bifurcation and stability of bifurcation periodic solutions is given by applying the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical results are also provided.