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Remerging Feigenbaum Trees, Coexisting Behaviors and Bursting Oscillations in a Novel 3D Generalized Hopfield Neural Network

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Abstract

This paper, a novel 3D generalized Hopfield neural network is proposed and investigated in order to generate and highlight some unknown behaviors related to such type of neural network. This generalized model is constructed by exploiting the effect of an external stimulus on the dynamics of a simplest 3D autonomous Hopfield neural network reported to date. The stability of the model around its ac-equilibrium point is studied. We note that the model has three types of stability depending on the value of the external stimulus. The stable node-focus, the unstable saddle focus, and the stable node characterize the stability of the equilibrium point of the model. Traditional nonlinear analyses tools are used to highlight and support several complex phenomena such as remerging Feigenbaum trees, the coexistence of up to two, four and six disconnected stable states when the amplitude of the external stimulus is set to zero. Furthermore, for some values of the frequency and amplitudes of the external stimulus, bursting oscillations occur. This latter behavior is characterized by the fact that oscillations switch between quiescent states and spiking states, repetitively. The transformed phase portraits are used to support the bursting mode of oscillations found. Finally, PSpice simulations enable to support the results of the theoretical studies.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon

    Z. Tabekoueng Njitacke

  2. Unité de Recherche d’Automatique et Informatique Appliquée (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, Université de Dschang, Dschang, Cameroon

    Z. Tabekoueng Njitacke, C. Laura Matze, M. Fouodji Tsotsop & J. Kengne

  3. Unité de Recherche de Matière Condensée, d’Electronique et de Traitement du Signal (LAMACETS), Department of Physics, Université de Dschang, P.O. Box 67, Dschang, Cameroon

    C. Laura Matze & M. Fouodji Tsotsop

Authors
  1. Z. Tabekoueng Njitacke
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  2. C. Laura Matze
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  3. M. Fouodji Tsotsop
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  4. J. Kengne
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Correspondence to Z. Tabekoueng Njitacke.

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Tabekoueng Njitacke, Z., Laura Matze, C., Fouodji Tsotsop, M. et al. Remerging Feigenbaum Trees, Coexisting Behaviors and Bursting Oscillations in a Novel 3D Generalized Hopfield Neural Network. Neural Process Lett 52, 267–289 (2020). https://doi.org/10.1007/s11063-020-10264-1

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  • DOI: https://doi.org/10.1007/s11063-020-10264-1

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