High codimensional bifurcation analysis to a six-neuron BAM neural network

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• 作者：Yanwei Liu ; Shanshan Li ; Zengrong Liu ; Ruiqi Wang
• 关键词：Neural networks ; Bogdanov–Takens bifurcation ; Triple zero bifurcation
• 刊名：Cognitive Neurodynamics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：10
• 期：2
• 页码：149-164
• 全文大小：1,024 KB
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• 作者单位：Yanwei Liu (1)
  Shanshan Li (2)
  Zengrong Liu (1)
  Ruiqi Wang (1)
  
  1. Department of Mathematics of Shanghai University, Shanghai, 200444, China
  2. Institute of Systems Biology, Shanghai University, Shanghai, 200444, China
  
• 刊物主题：Biomedicine general; Neurosciences; Computer Science, general; Artificial Intelligence (incl. Robotics); Biochemistry, general; Cognitive Psychology;
• 出版者：Springer Netherlands
• ISSN：1871-4099

文摘

In this article, the high codimension bifurcations of a six-neuron BAM neural network system with multiple delays are addressed. We first deduce the existence conditions under which the origin of the system is a Bogdanov–Takens singularity with multiplicities two or three. By choosing the connection coefficients as bifurcation parameters and using the formula derived from the normal form theory and the center manifold, the normal forms of Bogdanov–Takens and triple zero bifurcations are presented. Some numerical examples are shown to support our main results.