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Infinitely many coexisting hidden attractors in a new hyperbolic-type memristor-based HNN

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Abstract

In this article, a new model of Hopfield Neural Network (HNN) with two neurons considering a synaptic weight with a hyperbolic-type memristor is studied. Equilibrium points analysis shows that the system has an unstable line of equilibrium in the absence of the external stimuli (i.e. \(I_{1} =0)\) and presents no equilibrium point in the presence of the external stimuli (i.e. \(I_{1} \ne 0)\); hence the model admits hidden attractors. Analyses are carried out for both cases \(I_{1} =0\) and \(I_{1} \ne 0\) using appropriate tools (bifurcation diagrams and the Lyapunov exponents, phase portraits, etc.). For both modes of operations, the system exhibits complex homogeneous and heterogeneous bifurcations, respectively marked by a large number of coexisting attractors. The roads to chaos unfold in the same scenario of period doubling. The Hamiltonian plot for the case \(I_{1} =0\) allows us to observe an increase in the energy of the neuronal structure when it migrates from regular oscillations to irregular ones. Moreover, the existence of infinitely many coexisting homogeneous solutions (chaotic or periodic) is revealed for case \(I_{1} =0\). In contrast, for \(I_{1} \ne 0\) (i.e \(I_{1} =0.1)\) the new model presents infinitely many coexisting hidden heterogeneous attractors (periodic and chaotic). An electronic circuit design of the new hyperbolic memristor enables the analog computer of the whole system to be designed for future engineering applications. Simulation results based on this analog computer in PSpice confirm those of the numerical investigations.

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Acknowledgements

This work is partially funded by Center for Nonlinear Systems, Chennai Institute of Technology, India vide funding number CIT/CNS/2021/RD/022.

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Authors and Affiliations

  1. Research Unit of Automation and Applied Computer (URAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon

    Isaac Sami Doubla & Jacques Kengne

  2. Research Unit of Condensed Matter, Electronics and Signal Processing (UR-MACETS) Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Isaac Sami Doubla

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

    Zeric Njitacke Tabekoueng

  4. Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, Tamilnadu, India

    Balamurali Ramakrishnan & Karthikeyan Rajagopal

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Doubla, I.S., Ramakrishnan, B., Tabekoueng, Z.N. et al. Infinitely many coexisting hidden attractors in a new hyperbolic-type memristor-based HNN. Eur. Phys. J. Spec. Top. 231, 2371–2385 (2022). https://doi.org/10.1140/epjs/s11734-021-00372-x

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