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Reversal of period-doubling and extreme multistability in a novel 4D chaotic system with hyperbolic cosine nonlinearity

  • V. R. Folifack SigningEmail author
  • J. Kengne
Article
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Abstract

Recently, the study of nonlinear systems with an infinite number of coexisting attractors has become one of the most followed topics owing to their fundamental and technological importance. This contribution is focused on a new 4D autonomous system (whose nonlinearity is a hyperbolic function) inspired by the quadratic system introduced by Jay and Roy (Optik, http://dx.doi.org/ https://doi.org/10.1016/j.ijleo.2017.07.042, 2017). Basic properties of the new system are discussed and its complex behaviors are characterized using classical nonlinear diagnostic tools. This system exhibits a rich repertoire of dynamic behaviors including chaos, chaos 2-torus, and quasi-periodicity. Interesting and striking phenomena such as antimonotonicity and extreme multistability are reported. Moreover, the hyperbolic cosine nonlinearity is easily implemented by using only two semiconductor diodes (no analog multiplier is involved) connected in parallel. We confirm the feasibility of the proposed theoretical model using PSpice simulations based on an analog computer of the model.

Keywords

4D chaotic system Antimonotonicity Extreme multistability Hyperbolic cosine nonlinearity PSpice simulations 

Notes

Acknowledgements

The authors would like to thank the editor and the anonymous reviewers for their valuable comments and suggestions that helped to greatly improve this work.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Unité de Recherche de Laboratoire d’Automatique et Informatique Appliquée (LAIA), Department of Electrical EngineeringIUT-FV Bandjoun, University of DschangDschangCameroon
  2. 2.Unité de Recherche de Matière Condensée, d’Electronique et de Traitement du Signal, Department of PhysicsUniversity of DschangDschangCameroon

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