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Dynamical analysis and multistability in autonomous hyperchaotic oscillator with experimental verification

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Abstract

In this contribution, a modified oscillator of Tamasevicius et al. (Electron Lett 33:542–544, 1997) (referred to as the mTCMNL oscillator hereafter) is introduced with antiparallel diodes as nonlinear elements. The model is described by a continuous time of four-dimensional autonomous system with hyperbolic sine nonlinearity based on Shockley diode model. Various methods for characterizing chaos/hyperchaos including bifurcation diagrams, Lyapunov exponents spectrum, frequency spectra, phase portraits, Poincaré sections and two parameter Lyapunov exponents diagrams are exploited to point out the rich dynamical behaviors in the model. Numerical results indicate that the system displays extremely rich dynamical behaviors including periodic windows, torus, chaotic and hyperchaotic oscillations. One of the main findings of this work is the presence of a region in the parameter space in which the mTCMNL experiences hysteretic behaviors. This later singularity/phenomenon is marked by the coexistence of multiple attractors (i.e., coexistence of asymmetric pair of periodic, torus and chaotic attractors with symmetric periodic, torus and chaotic attractors), for the same parameters settings. Basins of attractions of various competing attractors depicts symmetric complex basin boundaries, thus suggesting possible jumps between coexisting solutions (i.e., asymmetric pair of attractors with symmetric one) in experiments. A predominant route to chaos/hyperchaos observed in the system for different system parameters is the Afraimovich–Shilnikov scenario with tiny periodic regions. Experimental results from real-time circuit implementation are in good agreement with numerical analysis.

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Acknowledgements

T. F. Fonzin acknowledges firstly DST-FICCI through the C V Raman International Fellowship for African Researchers (INT /NAI/CVRF/2014) for the financial support. Secondly, he acknowledges Mr. Danda Samuel and Mr. Jiogo Guy from National Advanced School of Post and Telecommunication (SUP’PTIC) of Yaoundé-Cameroon for the material grant necessary for experimental analysis. Also, he acknowledges Prof. M. Lakshmanan, Dr. A. Venkatesan and Dr. K. Suresh from Centre for Nonlinear Dynamics (CNLD), Tiruchirappalli, India, for all the helpful discussions and readings. Finally, authors would like to convey thanks to the anonymous reviewers for their useful suggestions and comments that helped to improve the content of the present manuscript.

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Authors and Affiliations

  1. Unité de recherche de Matière Condensée d’Electronique et de Traitement de Signal (LAMACETS), Faculty of Sciences, University of Dschang, P. O. Box 67, Dschang, Cameroon

    T. Fozin Fonzin

  2. Centre for Nonlinear Dynamics (CNLD), School of Physics, Bharathidasan University, Tiruchirappalli, 620 024, India

    T. Fozin Fonzin

  3. Centre d’Excellence Africain en Technologies de l’Information et de la Communication (CETIC), University of Yaoundé I, P. O. Box 812, Yaoundé, Cameroon

    T. Fozin Fonzin

  4. Unité de recherche d’Automatique et d’informatique Appliquée (LAIA), IUT-FV de Bandjoun, University of Dschang, P. O. Box 134, Bandjoun, Cameroon

    J. Kengne

  5. Unité de recherche de Mécanique et de Modélisation des Systèmes Physiques (L2MSP), Faculty of Sciences, University of Dschang, P. O. Box 69, Dschang, Cameroon

    F. B. Pelap

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  1. T. Fozin Fonzin
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Fozin Fonzin, T., Kengne, J. & Pelap, F.B. Dynamical analysis and multistability in autonomous hyperchaotic oscillator with experimental verification. Nonlinear Dyn 93, 653–669 (2018). https://doi.org/10.1007/s11071-018-4216-z

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