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A simple Jerk-like system without equilibrium: Asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees

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  • Zhang, Sen
  • Zeng, Yicheng

Abstract

The topic associated with hidden attractor and multistability has been received considerable attention recently. In this paper, a novel no-equilibrium Jerk-like chaotic system is constructed and explored. Particularly, owing to the absence of the equilibria, such a new system can be categorized as a system with hidden attractors. More interestingly, this system holds three conspicuous characteristics. The first one is that various asymmetric coexisting hidden attractors and complicated transient chaos behaviors are obtained. The second one is the new finding of the periodic bursting oscillation and unusual phenomenon of transient periodic bursting oscillation in the system. The third one is the observation of the amazing and rare phenomenon of one to two full Feigenbaum remerging trees, namely, antimonotonicity. To the best knowledge of us, the last two special features are first discovered and have never been reported, especially in such no-equilibrium chaotic system that exhibits hidden attractors. With the help of phase portraits, time series, bifurcation diagram, Lyapunov exponents, chaotic dynamical diagram, basin of attraction and so forth, the rich hidden dynamical properties of this system are systematically analyzed and investigated. Additionally, a hardware electronic circuit on a breadboard is carried out. A very good similarity between the hardware experimental results and the theoretical analysis testifies the feasibility and practicality of this original system.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:120:y:2019:i:c:p:25-40
    DOI: 10.1016/j.chaos.2018.12.036
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    6. Ramadoss, Janarthanan & Kengne, Jacques & Koinfo, Jean Baptiste & Rajagopal, Karthikeyan, 2022. "Multiple Hopf bifurcations, period-doubling reversals and coexisting attractors for a novel chaotic jerk system with Tchebytchev polynomials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    7. Zuolei Wang & Lizhou Zhuang & Jianjiang Yu & Haibo Jiang & Wanjiang Xu & Xuerong Shi, 2023. "Hidden Dynamics of a New Jerk-like System with a Smooth Memristor and Applications in Image Encryption," Mathematics, MDPI, vol. 11(22), pages 1-18, November.
    8. Yamina Soula & Hadi Jahanshahi & Abdullah A. Al-Barakati & Irene Moroz, 2023. "Dynamics and Global Bifurcations in Two Symmetrically Coupled Non-Invertible Maps," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    9. Sun, Xi & Yan, Shaohui & Zhang, Yuyan & Wang, Ertong & Wang, Qiyu & Gu, Binxian, 2022. "Bursting dynamics and the zero-Hopf bifurcation of simple jerk system," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
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    11. Peng, Xuenan & Zeng, Yicheng, 2020. "Image encryption application in a system for compounding self-excited and hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    12. Bo Sang & Bo Huang, 2020. "Zero-Hopf Bifurcations of 3D Quadratic Jerk System," Mathematics, MDPI, vol. 8(9), pages 1-19, August.
    13. Chen, Mo & Wang, Ankai & Wang, Chao & Wu, Huagan & Bao, Bocheng, 2022. "DC-offset-induced hidden and asymmetric dynamics in Memristive Chua's circuit," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    14. Rech, Paulo C., 2022. "Self-excited and hidden attractors in a multistable jerk system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    15. Trikha, Pushali & Mahmoud, Emad E. & Jahanzaib, Lone Seth & Matoog, R.T. & Abdel-Aty, Mahmoud, 2021. "Fractional order biological snap oscillator: Analysis and control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
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