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Antimonotonicity, chaos, quasi-periodicity and coexistence of hidden attractors in a new simple 4-D chaotic system with hyperbolic cosine nonlinearity

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  • Signing, V.R. Folifack
  • Kengne, J.
  • Pone, J.R. Mboupda

Abstract

Recently, the study of systems with hidden attractors has become one of the most followed topics owing to their fundamental and technological importance. This contribution is focused on a new simple 4-D chaotic system (whose nonlinearity is a hyperbolic function) inspired by the quadratic system introduced by [Jay and Roy Nonlinear Dyn (2017) 89:1845–1862]. Basic properties of the new system are discussed and its complex behaviors are characterized using dynamic systems analysis tools. This system exhibits a rich repertoire of dynamic behaviors including chaos, chaos 2-torus, and quasi-periodic. Other interesting phenomena such as multistability, antimonotonicity, and torus-doubling bifurcations are also reported. Moreover, the hyperbolic cosine nonlinearity is easily implemented by using a pair of semiconductor diodes (no analog multiplier is involved). We confirm the feasibility of the proposed theoretical model using PSpice simulations and a physical realization based on an electronic analog implementation of the model.

Suggested Citation

  • Signing, V.R. Folifack & Kengne, J. & Pone, J.R. Mboupda, 2019. "Antimonotonicity, chaos, quasi-periodicity and coexistence of hidden attractors in a new simple 4-D chaotic system with hyperbolic cosine nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 187-198.
    • Handle: RePEc:eee:chsofr:v:118:y:2019:i:c:p:187-198
    DOI: 10.1016/j.chaos.2018.10.018
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    References listed on IDEAS

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    1. Njitacke, Z.T. & kengne, J. & Kengne, L. Kamdjeu, 2017. "Antimonotonicity, chaos and multiple coexisting attractors in a simple hybrid diode-based jerk circuit," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 77-91.
    2. Singh, Jay Prakash & Roy, B.K., 2016. "The nature of Lyapunov exponents is (+, +, −, −). Is it a hyperchaotic system?," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 73-85.
    3. Ojoniyi, Olurotimi S. & Njah, Abdulahi N., 2016. "A 5D hyperchaotic Sprott B system with coexisting hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 172-181.
    4. Qi, Guoyuan & Chen, Guanrong & Zhang, Yuhui, 2008. "On a new asymmetric chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 409-423.
    5. Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
    6. Leutcho, G.D. & Kengne, J. & Kengne, L. Kamdjeu, 2018. "Dynamical analysis of a novel autonomous 4-D hyperjerk circuit with hyperbolic sine nonlinearity: Chaos, antimonotonicity and a plethora of coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 67-87.
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    Cited by:

    1. Jiri Petrzela, 2022. "Chaos in Analog Electronic Circuits: Comprehensive Review, Solved Problems, Open Topics and Small Example," Mathematics, MDPI, vol. 10(21), pages 1-28, November.
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    4. Chen, Mo & Ren, Xue & Wu, Huagan & Xu, Quan & Bao, Bocheng, 2020. "Interpreting initial offset boosting via reconstitution in integral domain," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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