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Symmetry Breaking-Induced Dynamics for a Fourth-Order Memristor-Based Chaotic Circuit

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Abstract

Nonlinear dynamical systems with symmetry have been studied extensively yielding rich and striking bifurcation patterns such as period-doubling sequence, merging crisis, crisis-induced intermittency, spontaneous symmetry breaking, and coexisting pairs of mutually symmetric attractors as well. However, very little is known unfortunately about the behavior of such systems in the presence of an explicit symmetry breaking perturbation. In this work, we evaluate the impact of an explicit symmetry break on the dynamics of a fourth-order autonomous memristive chaotic circuit. The symmetry break is obtained by assuming different electrical properties for the two pairs of diodes forming the generalized memristor. Thus, the generalized memristor exhibits an asymmetric pinched hysteresis loop which induces the asymmetry of the whole jerk circuit. We demonstrate that the symmetry break induces new and extremely complex patterns including critical phenomena, coexisting bubbles of different periodicity, multiple coexisting nonsymmetric attractors, just to name a few. These features are highlighted by using phase portraits, basins of attraction, bifurcation diagrams, and plots of largest Lyapunov exponents as main tools. A series of laboratory experimental tests are carried out to support the theoretical analysis.

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Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work is partially funded by Centre for Nonlinear Systems, Chennai Institute of Technology, India, vide funding number CIT/CNS/2022/RD/006. The authors would like to thank the anonymous reviewers for their comments and suggestions that helped to greatly improve the content of the present manuscript.

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Authors and Affiliations

  1. Laboratoire d’Automatique Et Informatique Appliquée (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang Cameroon, Dschang, Cameroon

    Léandre Kamdjeu Kengne & Jacques Kengne

  2. Laboratory of Electronics and Signal Processing, Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Léandre Kamdjeu Kengne & Jacques Kengne

  3. Center for Artificial Intelligence, Chennai Institute of Technology, Chennai, India

    Janarthanan Ramadoss

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

    Karthikeyan Rajagopal

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  1. Léandre Kamdjeu Kengne
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Correspondence to Jacques Kengne.

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Kengne, L.K., Ramadoss, J., Kengne, J. et al. Symmetry Breaking-Induced Dynamics for a Fourth-Order Memristor-Based Chaotic Circuit. Circuits Syst Signal Process 41, 3706–3738 (2022). https://doi.org/10.1007/s00034-022-01976-x

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