Dynamics, control and symmetry breaking aspects of an infinite-equilibrium chaotic system

Abstract

It is well known that the symmetry break deliberately induced in a nonlinear system may help to discover new nonlinear patterns. In this work, we investigate the impact of an explicit symmetry break on the dynamics of a recently introduced chaotic system with a curve of equilibriums (Pham et al. in Circuits Syst Signal Process 37(3):1028–1043, 2018). We demonstrate that the symmetry break engenders rich and striking nonlinear phenomena including the coexistence of multiple asymmetric stable states, the presence of parallel bifurcation branches, hysteresis, and critical transitions as well. A simple control strategy based on linear augmentation technique that enables to drive the system from the state of four coexisting self-excited attractors to a monostable state is successfully adapted. To the best of the authors’ knowledge, this work represents the first report on symmetry breaking for a chaotic system with infinite equilibriums and thus deserves dissemination.

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Acknowledgements

L. Kamdjeu Kengne would like to thank Pr. Fotsin Hilaire Bertrand (University of Dschang, Cameroon), Dr. Fozin Fonzin Theophile (University of Buea, Cameroon) and Dr. Tabekoueng Njitacke Zeric (University of Buea, Cameroon) for the helpful discussions. 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 Leandre Kamdjeu Kengne.

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Kamdjeu Kengne, L., Kengne, J., Mboupda Pone, J.R. et al. Dynamics, control and symmetry breaking aspects of an infinite-equilibrium chaotic system. Int. J. Dynam. Control 8, 741–758 (2020). https://doi.org/10.1007/s40435-020-00613-2

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Keywords

  • Chaotic system with infinite equilibriums
  • Explicit symmetry breaking
  • Coexisting multiple asymmetric attractors
  • Basins of attraction
  • Critical transitions