Bifurcation behaviors of an Euler discretized inertial delayed neuron model

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• 作者：Xing He ; ChuanDong Li ; TingWen Huang ; JunZhi Yu
• 关键词：resonance bifurcation ; Euler discretized ; inertial delayed neural network
• 刊名：SCIENCE CHINA Technological Sciences
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：59
• 期：3
• 页码：418-427
• 全文大小：1,105 KB
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• 作者单位：Xing He (1)
  ChuanDong Li (1)
  TingWen Huang (2)
  JunZhi Yu (3)
  
  1. School of Electronics and Information Engineering, Southwest University, Chongqing, 400715, China
  2. Texas A & M University at Qatar, Doha, 5825, Qatar
  3. State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China
  
• 刊物类别：Engineering
• 刊物主题：Chinese Library of Science
  Engineering, general
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1900

文摘

This paper presents an Euler discretized inertial delayed neuron model, and its bifurcation dynamical behaviors are discussed. By using the associated characteristic model, center manifold theorem and the normal form method, it is shown that the model not only undergoes codimension one (flip, Neimark-Sacker) bifurcation, but also undergoes cusp and resonance bifurcation (1:1 and 1:2) of codimension two. Further, it is found that the parity of delay has some effect on bifurcation behaviors. Finally, some numerical simulations are given to support the analytic results and explore complex dynamics, such as periodic orbits near homoclinic orbits, quasiperiodic orbits, and chaotic orbits.