Dynamical analysis of a novel 4-neurons based Hopfield neural network: emergences of antimonotonicity and coexistence of multiple stable states

  • Z. T. NjitackeEmail author
  • J. Kengne
  • T. Fonzin Fozin
  • B. P. Leutcha
  • H. B. Fotsin


In this contribution, we investigate the dynamics of a novel model of 4-neurons based Hopfield neural networks. Our analyses highlight complex phenomena such as chaotic and periodic behaviors which have been classified by Panahi et al. (Chaos Solitons Fractals 105:150–156, 2017) as some brain behaviors. More interestingly, it has been revealed several sets of synaptic weights matrix for which the proposed HNNs displays multiple coexisting stable states including two, four and six disjoined orbits. Basins of attraction of coexisting stable states have been computed showing different regions in which each solution can be captured. Beside the presence of coexisting bifurcations, the model displays remerging Feigenbaum trees bifurcations also known as antimonotonicity for some judicious sets of synaptic weights. PSpice investigations are finally used to confirm results of the theoretical investigations.


4-Neurons based HNN Antimonotonicity Coexistence of multiple stable states Basin of attraction Pspice simulations 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Z. T. Njitacke
    • 1
    • 2
    Email author
  • J. Kengne
    • 1
  • T. Fonzin Fozin
    • 1
    • 2
  • B. P. Leutcha
    • 3
  • H. B. Fotsin
    • 2
  1. 1.Unité de Recherche d’Automatique et Informatique Appliquée (LAIA), Department of Electrical Engineering, IUT-FV BandjounUniversity of DschangDschangCameroon
  2. 2.Unité de Recherche de Matière Condensée, d’Electronique et de Traitement du Signal (LAMACETS), Department of PhysicsUniversity of DschangDschangCameroon
  3. 3.Department of Chemistry, Faculty of ScienceThe University of MarouaMarouaCameroon

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