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Period-doubling route to chaos, bistability and antimononicity in a jerk circuit with quintic nonlinearity

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Abstract

In this paper, the dynamics of an autonomous jerk circuit with quintic nonlinearity is investigated. The circuit is described by a set of three coupled-first order nonlinear differential equations recently introduced as memory oscillator by Sprott (Elegant chaos, algebraically simple chaotic flows, World Scientific, Singapore, 2010). The dynamical behaviors of the system are examined with the help of common nonlinear methods such as bifurcation diagrams, largest Lyapunov exponent plot, Poincaré map as well as power density spectra. It is revealed that the system under scrutiny experiences some complex phenomena including period-doubling route to chaos, bistability and antimonotonicity. Finally, the analog simulations are carried out in PSIM and experimental electronic circuit is realized to validate the numerical results.

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Acknowledgements

The authors would like to thank Prof. Woafo Paul of University of Yaoundé 1-Cameroon, for suggesting many helpful pieces of advice during the investigation of the work and Dr. Sifeu Takougang Kingni of University of Maroua-Cameroon, for carefully reading the manuscript.

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Authors and Affiliations

  1. Research Unit of Laboratory of Automation and Applied Computer (LAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon

    Justin Roger Mboupda Pone & Guillaume Honore Kom

  2. Laboratory of Energetic and Automation (LEA), Automation and Control Laboratory Team (ACL), Electrical Engineering Department of National Advanced School of Engineering, ENSP, University of Yaoundé I, P.O. Box 8390, Yaoundé, Cameroon

    Justin Roger Mboupda Pone

  3. Research Unit of Laboratory of Condensed Matter, Electronics and Signal Processing (LAMACETS) Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Victor Kamdoum Tamba

  4. Laboratory of Electronics and Signal Processing (LETS), GRETMAT Team, Electrical Engineering Department of National Advanced School of Engineering, ENSP, University of Yaoundé I, P.O. Box 8390, Yaoundé, Cameroon

    Guillaume Honore Kom & Alain Bertin Tiedeu

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  1. Justin Roger Mboupda Pone
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  2. Victor Kamdoum Tamba
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  3. Guillaume Honore Kom
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Correspondence to Justin Roger Mboupda Pone.

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Mboupda Pone, J.R., Kamdoum Tamba, V., Kom, G.H. et al. Period-doubling route to chaos, bistability and antimononicity in a jerk circuit with quintic nonlinearity. Int. J. Dynam. Control 7, 1–22 (2019). https://doi.org/10.1007/s40435-018-0431-1

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