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Bifurcation analysis on a generalized recurrent neural network with two interconnected three-neuron components

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  • Hajihosseini, Amirhossein
  • Maleki, Farzaneh
  • Rokni Lamooki, Gholam Reza

Abstract

A class of recurrent neural networks is constructed by generalizing a specific class of n-neuron networks. It is shown that the newly constructed network experiences generic pitchfork and Hopf codimension one bifurcations. It is also proved that the emergence of generic Bogdanov–Takens, pitchfork–Hopf and Hopf–Hopf codimension two, and the degenerate Bogdanov–Takens bifurcation points in the parameter space is possible due to the intersections of codimension one bifurcation curves. The occurrence of bifurcations of higher codimensions significantly increases the capability of the newly constructed recurrent neural network to learn broader families of periodic signals.

Suggested Citation

  • Hajihosseini, Amirhossein & Maleki, Farzaneh & Rokni Lamooki, Gholam Reza, 2011. "Bifurcation analysis on a generalized recurrent neural network with two interconnected three-neuron components," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 1004-1019.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:11:p:1004-1019
    DOI: 10.1016/j.chaos.2011.08.006
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    References listed on IDEAS

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    1. Huang, Zai-Tang & Yang, Qi-Gui & Luo, Xiao-shu, 2008. "Exponential stability of impulsive neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 770-780.
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