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Neural Processing Letters

, Volume 50, Issue 3, pp 2219–2245 | Cite as

Bifurcation Analysis for Simplified Five-Neuron Bidirectional Associative Memory Neural Networks with Four Delays

  • Changjin XuEmail author
  • Maoxin Liao
  • Peiluan Li
  • Ying Guo
Article
First Online:

Abstract

The paper deals with the stability and bifurcation analysis of a class of simplified five-neuron bidirectional associative memory neural networks with four delays. By discussing the characteristic transcendental equation and applying Hopf bifurcation theory, some sufficient conditions which guarantee the local stability and the existence of Hopf bifurcation of the neural networks are established. With the aid of the normal form theory and center manifold theory, we obtain some specific formulae to determine the stability and the direction of the Hopf bifurcation. Computer simulations are implemented to explain the key mathematical predictions. The paper ends with a brief conclusion.

Keywords

BAM neural networks Stability Hopf bifurcation Time delay 
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Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Changjin Xu
    • 1
    Email author
  • Maoxin Liao
    • 2
  • Peiluan Li
    • 3
  • Ying Guo
    • 4
  1. 1.Guizhou Key Laboratory of Economics System SimulationGuizhou University of Finance and EconomicsGuiyangPeople’s Republic of China
  2. 2.School of Mathematics and PhysicsUniversity of South ChinaHengyangPeople’s Republic of China
  3. 3.School of Mathematics and StatisticsHenan University of Science and TechnologyLuoyangPeople’s Republic of China
  4. 4.School of Information Science and EngineeringCentral South UniversityChangshaPeople’s Republic of China

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