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Bistable Hidden Attractors in a Novel Chaotic System with Hyperbolic Sine Equilibrium

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Abstract

For the past 4 years, there has been a rapid rise in the study of chaotic systems with curves of equilibria which are categorized as systems with hidden attractors. There is still significant controversy surrounding the shapes of equilibrium points. This paper presents a new three-dimensional autonomous chaotic system with hyperbolic sine equilibrium. Fundamental dynamical properties and complex dynamics of the system have been discovered by using equilibrium analysis, phase portrait, Poincaré map, bifurcation diagram and Lyapunov spectrum. It is crucial to note that there are bistable hidden chaotic attractors in the introduced system. Furthermore, in order to show the feasibility of the new system with hyperbolic sine equilibrium, its electronic circuit has been implemented.

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Acknowledgements

The authors would like to thank the Editor and Reviewers for their invaluable comments and suggestions on the article. The authors acknowledge Prof. GuanRong Chen, Department of Electronic Engineering, City University of Hong Kong, for suggesting many helpful references. This work has been supported by the Polish National Science Centre, MAESTRO Programme Project No. 2013/08/A/ST8/00/780.

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Authors and Affiliations

  1. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam

    Viet-Thanh Pham

  2. Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924, Lodz, Poland

    Viet-Thanh Pham & Tomasz Kapitaniak

  3. Department of Physics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Christos Volos

  4. Department of Mechanical and Electrical Engineering, Institute of Mines and Petroleum Industries, University of Maroua, Maroua, Cameroon

    Sifeu Takougang Kingni

  5. Biomedical Engineering Department, Amirkabir University of Technology, 15875-4413, Tehran, Iran

    Sajad Jafari

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  1. Viet-Thanh Pham
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  2. Christos Volos
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  4. Tomasz Kapitaniak
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Correspondence to Viet-Thanh Pham.

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Pham, VT., Volos, C., Kingni, S.T. et al. Bistable Hidden Attractors in a Novel Chaotic System with Hyperbolic Sine Equilibrium. Circuits Syst Signal Process 37, 1028–1043 (2018). https://doi.org/10.1007/s00034-017-0611-9

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