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

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Abstract

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.

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Authors and Affiliations

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

    Z. T. Njitacke, J. Kengne & T. Fonzin Fozin

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

    Z. T. Njitacke, T. Fonzin Fozin & H. B. Fotsin

  3. Department of Chemistry, Faculty of Science, The University of Maroua, P. O. Box 46, Maroua, Cameroon

    B. P. Leutcha

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  1. Z. T. Njitacke
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  2. J. Kengne
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  3. T. Fonzin Fozin
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  4. B. P. Leutcha
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  5. H. B. Fotsin
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Correspondence to Z. T. Njitacke.

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Njitacke, Z.T., Kengne, J., Fozin, T.F. et al. Dynamical analysis of a novel 4-neurons based Hopfield neural network: emergences of antimonotonicity and coexistence of multiple stable states. Int. J. Dynam. Control 7, 823–841 (2019). https://doi.org/10.1007/s40435-019-00509-w

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