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Effects of symmetry-breaking on the dynamics of the Shinriki’s oscillator

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Abstract

We investigate the dynamics of the well-known Shinriki’s oscillator both in its symmetric and asymmetric modes of operation. Instead of using the classical approximate cubic model of the Shinriki’s oscillator, we propose a close form model by exploiting the Shockley exponential diode equation. The proposed model takes into account the intrinsic characteristics of semiconductor diodes forming the nonlinear part (i.e., the positive conductance). We address the realistic issue of symmetry-breaking by considering different numbers of diodes within the two branches of the positive conductance. The dynamics of the system is investigated by exploiting conventional nonlinear analysis tools such as bifurcation diagrams, phase-space trajectories plots, basins of attractions, and graphs of Lyapunov exponent as well. In the symmetric mode of operation, the system experiences coexisting symmetric attractors, period-doubling route to chaos, and merging crisis. The symmetry breaking analysis yields two asymmetric coexisting bifurcation branches (i.e., asymmetric bi-stability) each of which exhibits its own sequence of bifurcations to chaos when monitoring the main control parameter. In this special mode, the merging process never occurs; instead, one of the bifurcation branches vanishes when decreasing the control parameter beyond a critical value following a crisis event. The theoretical results are validated by carrying out laboratory experimental studies of the physical circuit.

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My manuscript has no associated data or the data will not be deposited.

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Acknowledgements

All authors would like to thanks the anonymous reviewers for their constructive comments, critics, and suggestions that helped to improve the content of the present paper.

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Authors and Affiliations

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

    Léandre Kamdjeu Kengne & Romanic Kengne

  2. Unité de Recherche d’Automatique et Informatique Appliquée (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, P.O. Box 134, Bandjoun, Cameroon

    Léandre Kamdjeu Kengne & Roger Mboupda Pone

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

    Zeric Tabekoueng Njitacke

  4. Department of Electrical and Electronic Engineering, Faculty of Engineering and Technology (FET), University of Buea, P.O. Box 63, Buea, Cameroon

    Theophile Fozin Fonzin

  5. Unité de Recherche de Mécanique et de Modélisation des Systèmes Physiques (UR-2MSP), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Hervé Thierry Kamdem Tagne

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  1. Léandre Kamdjeu Kengne
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All authors have contributed equally for the preparation of the manuscript.

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Correspondence to Léandre Kamdjeu Kengne.

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Kengne, L.K., Kengne, R., Njitacke, Z.T. et al. Effects of symmetry-breaking on the dynamics of the Shinriki’s oscillator. Eur. Phys. J. Spec. Top. 230, 1813–1827 (2021). https://doi.org/10.1140/epjs/s11734-021-00130-z

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