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

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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.

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Authors and Affiliations

  1. Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, 550004, People’s Republic of China

    Changjin Xu

  2. School of Mathematics and Physics, University of South China, Hengyang, 421001, People’s Republic of China

    Maoxin Liao

  3. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, People’s Republic of China

    Peiluan Li

  4. School of Information Science and Engineering, Central South University, Changsha, 410083, People’s Republic of China

    Ying Guo

Authors
  1. Changjin Xu
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  2. Maoxin Liao
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  3. Peiluan Li
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  4. Ying Guo
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Correspondence to Changjin Xu.

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This work is supported by National Natural Science Foundation of China (No. 61673008) and Project of High-level Innovative Talents of Guizhou Province ([2016]5651) and Major Research Project of The Innovation Group of The Education Department of Guizhou Province ([2017]039), Project of Key Laboratory of Guizhou Province with Financial and Physical Features ([2017]004) and the Foundation of Science and Technology of Guizhou Province ([2018]1025 and [2018]1020).

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Xu, C., Liao, M., Li, P. et al. Bifurcation Analysis for Simplified Five-Neuron Bidirectional Associative Memory Neural Networks with Four Delays. Neural Process Lett 50, 2219–2245 (2019). https://doi.org/10.1007/s11063-019-10006-y

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