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Extremely rich dynamical behaviors in a simple nonautonomous Jerk system with generalized nonlinearity : hyperchaos, intermittency, offset-boosting and multistability

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Abstract

This paper investigates the extremely rich dynamical behaviors of the simple Jerk system as proposed by Volos et al. (Nonlinear Dyn 89(2):1047–1061, 2017) based on two main modifications: (i) introduction of a periodic sinusoidal external excitation in the system and (ii) generalization of the nonlinear function of the system in the form \(\varphi _k(x) = 0.5 (\exp (kx)-\exp (-x))\) as recently proposed by Kengne group (Negou and Kengne in AEU Int J Electron Commun 90:1–19, 2018). These changes are in origin of the observed rich dynamical behaviors including hyperchaos, chaos, intermittency, offset boosting and coexistence of multiple attractors. All these interesting dynamical behaviors are highlighted using the common dynamical tools such as bifurcation diagrams, spectrum of the Lyapunov exponents, two parameters diagrams, phase portraits and Poincaré sections. To the best of the author’s knowledge, the addition of an external force in the class of Jerk systems is new and has not been discussed earlier (despite the huge amount of related research works) and thus represents an enriching contribution to the understanding of the dynamics of Jerk’s system. The captured laboratory measurements are in perfect agreement with the theoretical analysis.

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Acknowledgements

A. Ngo Mouelas and T. Fonzin are grateful to Mr Tchagna Kouanou Aurelle from UR-MACETS for valuable discussions and reading of the manuscript. All 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 paper.

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Correspondence to T. Fonzin Fozin.

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Ngo Mouelas, A., Fonzin Fozin, T., Kengne, R. et al. Extremely rich dynamical behaviors in a simple nonautonomous Jerk system with generalized nonlinearity : hyperchaos, intermittency, offset-boosting and multistability. Int. J. Dynam. Control (2019). https://doi.org/10.1007/s40435-019-00530-z

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Keywords

  • Nonautonomous Jerk system
  • Hyperchaos
  • Multistability
  • Intermittency
  • Offset boosting
  • Experimental study