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Broken symmetry and dynamics of a memristive diodes bridge-based Shinriki oscillator

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  • Ramadoss, Janarthanan
  • Kengne, Jacques
  • Kengnou Telem, Adélaïde Nicole
  • Rajagopal, Karthikeyan

Abstract

We investigate the impact of a broken symmetry on the dynamics of the well-known Shinriki oscillator. The broken symmetry is caused by the memristive diodes bridge with an asymmetric pinched hysteresis loop current–voltage characteristic designed by selecting two pairs of semiconductor diodes with different electrical properties. We examine how the broken symmetry affects the topology of attractors, the nature of fixed points, the bifurcation structures, the number and types of coexisting solutions, and the topology of the basins of attraction as well. These features are highlighted by utilizing plots of Lyapunov exponents, bifurcation diagrams, basins of attraction and phase portraits. As sample results, up to four coexisting asymmetric chaotic and periodic attractors are reported following changes in both initial conditions and parameters. Moreover, some sets of parameters are revealed where the system develops the striking feature of coexisting bubbles of bifurcation. Breadboard experiments are carried out to support the theoretical investigations. Although the breaking of symmetry may be seen as a common practice to discover new nonlinear events, the results obtained in this work may help for a better understanding of the impact of a real memristor on the global behavior of chaotic oscillators including a memristor as nonlinear device.

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  • Ramadoss, Janarthanan & Kengne, Jacques & Kengnou Telem, Adélaïde Nicole & Rajagopal, Karthikeyan, 2022. "Broken symmetry and dynamics of a memristive diodes bridge-based Shinriki oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    • Handle: RePEc:eee:phsmap:v:588:y:2022:i:c:s0378437121008359
    DOI: 10.1016/j.physa.2021.126562
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    References listed on IDEAS

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    1. Gómez-Aguilar, J.F., 2020. "Chaos and multiple attractors in a fractal–fractional Shinriki’s oscillator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
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    4. Min, Fuhong & Zhang, Wen & Ji, Ziyi & Zhang, Lei, 2021. "Switching dynamics of a non-autonomous FitzHugh-Nagumo circuit with piecewise-linear flux-controlled memristor," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Kamdjeu Kengne, Léandre & Mboupda Pone, Justin Roger & Fotsin, Hilaire Bertrand, 2021. "On the dynamics of chaotic circuits based on memristive diode-bridge with variable symmetry: A case study," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
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