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Self-excited and hidden attractors in a multistable jerk system

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  • Rech, Paulo C.

Abstract

In this paper we investigate a jerk system which is modeled by a homogeneous third-order ordinary differential equation, with four parameters that control the dynamics. The proper choice of one of these parameters allows the system to display real or non-real equilibrium points. This implies that we can choose such a parameter so that the associated attractors are either self-excited or hidden. We consider the two situations, and investigate the dynamics of the two versions of this jerk system, in cross-sections of the three-dimensional parameter-space generated by the other three parameters. We show that both versions of the jerk system display multistability, with coexistence of periodic–periodic, chaotic–chaotic, and periodic–chaotic attractors in the phase-space, regardless of whether the attractors are self-excited or hidden. We also show that basins of attraction and attractors occupy smaller volumes in the case of the system with no equilibrium points.

Suggested Citation

  • Rech, Paulo C., 2022. "Self-excited and hidden attractors in a multistable jerk system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922007986
    DOI: 10.1016/j.chaos.2022.112614
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    References listed on IDEAS

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    1. Kenmogne, Fabien & Noubissie, Samuel & Ndombou, Guy Bertrand & Tebue, Eric Tala & Sonna, Armel Viquit & Yemélé, David, 2021. "Dynamics of two models of driven extended jerk oscillators: Chaotic pulse generations and application in engineering," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Chlouverakis, Konstantinos E. & Sprott, J.C., 2006. "Chaotic hyperjerk systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 739-746.
    3. Zhang, Sen & Zeng, Yicheng, 2019. "A simple Jerk-like system without equilibrium: Asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 25-40.
    4. Chiu, R. & López-Mancilla, D. & Castañeda, Carlos E. & Orozco-López, Onofre & Villafaña-Rauda, E. & Sevilla-Escoboza, R., 2019. "Design and implementation of a jerk circuit using a hybrid analog–digital system," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 255-262.
    5. Kengne, J. & Njikam, S.M. & Signing, V.R. Folifack, 2018. "A plethora of coexisting strange attractors in a simple jerk system with hyperbolic tangent nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 201-213.
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    Cited by:

    1. Isabelle L. Soares & Marcelo F. Krol & Paulo C. Rech, 2024. "Coexisting attractors and basins of attraction of an extended forced Duffing oscillator," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(6), pages 1-6, June.
    2. Chen, Chengjie & Min, Fuhong & Zhang, Yunzhen & Bao, Han, 2023. "ReLU-type Hopfield neural network with analog hardware implementation," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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