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On the Dynamics of Chua’s oscillator with a smooth cubic nonlinearity: occurrence of multiple attractors

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Abstract

Chua’s circuit is one of the well-known nonlinear circuits which have been used to study a rich variety of nonlinear dynamic behaviors such as bifurcation, chaos, and routes to chaos. In this work, I consider the dynamics of Chua’s circuit with a smooth cubic nonlinearity. The dynamics of the model is investigated using standard nonlinear analysis techniques including time series, bifurcation diagrams, phase space trajectories plots, Lyapunov exponents, and basins of attraction. Both period-doubling and crisis routes to chaos are reported. One of the major results of this work is the numerical finding of a parameter region in which Chua’s circuit experiences multiple attractors’ behavior (i.e., coexistence of four different periodic and chaotic attractors). This phenomenon was not reported previously in the Chua’s circuit (despite the huge amount of related research works) and thus represents an enriching contribution to the understanding of the dynamics of Chua’s oscillator. Basins of attraction of various coexisting attractors are depicted showing complex basin boundaries. The results obtained in this work let us conjecture that there are still some unknown and striking behaviors of Chua’s oscillator (e.g., the phenomenon of extreme multistability, i.e., infinitely many attractors) that need to be uncovered.

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Acknowledgments

The author is very grateful to anonymous referees for their valuable and critical comments which helped to improve the presentation of the paper. He also thanks Prof. Godpromesse Kenne (IUT-FV, University of Dschang) for interesting and enriching discussions.

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  1. Laboratoire d’Automatique et Informatique Appliquée (LAIA), Département de génie électrique, IUT-FV de Bandjoun, Université de Dschang, Dschang, Cameroun

    Jacques Kengne

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Correspondence to Jacques Kengne.

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Kengne, J. On the Dynamics of Chua’s oscillator with a smooth cubic nonlinearity: occurrence of multiple attractors. Nonlinear Dyn 87, 363–375 (2017). https://doi.org/10.1007/s11071-016-3047-z

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