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Extreme multi-stability: When imperfection changes quality

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  • Jafari, Sajad
  • Ahmadi, Atefeh
  • Panahi, Shirin
  • Rajagopal, Karthikeyan

Abstract

In this paper, we discuss how chaotic systems show the importance of imperfection. This happens through the butterfly effect. Then we discuss that chaotic systems with extreme multi-stability can much better demonstrate such importance. The reason is that in such systems not only the quantity of time-series is affected by butterfly effect, but also the quality of time-series is changed by small imperfections in parameters or initial conditions. We prove the importance of that difference better by comparing the efficiency of a newly proposed parameter estimation method on both an ordinary chaotic system and a chaotic system with extreme multi-stability.

Suggested Citation

  • Jafari, Sajad & Ahmadi, Atefeh & Panahi, Shirin & Rajagopal, Karthikeyan, 2018. "Extreme multi-stability: When imperfection changes quality," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 182-186.
    • Handle: RePEc:eee:chsofr:v:108:y:2018:i:c:p:182-186
    DOI: 10.1016/j.chaos.2018.02.005
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    Cited by:

    1. Bao, Han & Rong, Kang & Chen, Mo & Zhang, Xi & Bao, Bocheng, 2023. "Multistability and synchronization of discrete maps via memristive coupling," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Yunzhen Zhang & Zhong Liu & Mo Chen & Huagan Wu & Shengyao Chen & Bocheng Bao, 2019. "Dimensionality Reduction Reconstitution for Extreme Multistability in Memristor-Based Colpitts System," Complexity, Hindawi, vol. 2019, pages 1-12, November.
    3. Bao, H. & Gu, Y. & Xu, Q. & Zhang, X. & Bao, B., 2022. "Parallel bi-memristor hyperchaotic map with extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Bao, B. & Peol, M.A. & Bao, H. & Chen, M. & Li, H. & Chen, B., 2021. "No-argument memristive hyper-jerk system and its coexisting chaotic bubbles boosted by initial conditions," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Leutcho, Gervais Dolvis & Kengne, Jacques, 2018. "A unique chaotic snap system with a smoothly adjustable symmetry and nonlinearity: Chaos, offset-boosting, antimonotonicity, and coexisting multiple attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 275-293.
    6. Zhang, Yunzhen & Liu, Zhong & Wu, Huagan & Chen, Shengyao & Bao, Bocheng, 2019. "Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 354-363.
    7. Lai, Qiang & Yang, Liang & Liu, Yuan, 2022. "Design and realization of discrete memristive hyperchaotic map with application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    8. Wang, Zhen & Ahmadi, Atefeh & Tian, Huaigu & Jafari, Sajad & Chen, Guanrong, 2023. "Lower-dimensional simple chaotic systems with spectacular features," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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