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Multistability route in a PWL multi-scroll system through fractional-order derivatives

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  • Echenausía-Monroy, J.L.
  • Gilardi-Velázquez, H.E.
  • Wang, Ning
  • Jaimes-Reátegui, R.
  • García-López, J.H.
  • Huerta-Cuellar, G.

Abstract

Recently, it was discovered that the use of fractional derivatives induces the occurrence of multistable states in PWL systems with multiple scrolls. In this paper, we show the emergence of multistable states in a PWL system and study the route of the system to transition from monostable to multistable behavior by reducing the order of the fractional derivative. Using bifurcation diagrams that describe the evolution of the attractor as a consequence of the change in derivative order and basins of attraction, we show that the system has a path to multistability that reveals the mechanism for the occurrence of this behavior. The resulting dynamics shows the coexistence of up to n + 2 attractors, where n is the number of scrolls generated by the integer-order system, which has been confirmed for two different n-multi-scrolls systems. Moreover, the existence and uniqueness of the dynamics is proved by Poincaré sections, which show that the behaviors exist, and coexist, and are not a section of the same solution.

Suggested Citation

  • Echenausía-Monroy, J.L. & Gilardi-Velázquez, H.E. & Wang, Ning & Jaimes-Reátegui, R. & García-López, J.H. & Huerta-Cuellar, G., 2022. "Multistability route in a PWL multi-scroll system through fractional-order derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005653
    DOI: 10.1016/j.chaos.2022.112355
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    References listed on IDEAS

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    1. J. L. Echenausía-Monroy & C. A. Rodríguez-Martíne & L. J. Ontañón-García & J. Alvarez & J. Pena Ramirez & Atila Bueno, 2021. "Synchronization in Dynamically Coupled Fractional-Order Chaotic Systems: Studying the Effects of Fractional Derivatives," Complexity, Hindawi, vol. 2021, pages 1-12, December.
    2. Jesus M. Munoz-Pacheco & Luis Carlos Lujano-Hernández & Carlos Muñiz-Montero & Akif Akgül & Luis A. Sánchez-Gaspariano & Chun-Biao Li & Mustafa Çaǧri Kutlu & Carlos Aguilar-Ibanez, 2021. "Active Realization of Fractional-Order Integrators and Their Application in Multiscroll Chaotic Systems," Complexity, Hindawi, vol. 2021, pages 1-16, January.
    3. Ahmad, Shabir & Ullah, Aman & Akgül, Ali, 2021. "Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Gilardi-Velázquez, H.E. & Echenausía-Monroy, J.L. & Jaimes-Reátegui, R. & García-López, J.H. & Campos, Eric & Huerta-Cuellar, G., 2022. "Deterministic coherence resonance analysis of coupled chaotic oscillators: fractional approach," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Quan Xu & Xiao Tan & Yunzhen Zhang & Han Bao & Yihua Hu & Bocheng Bao & Mo Chen, 2020. "Riddled Attraction Basin and Multistability in Three-Element-Based Memristive Circuit," Complexity, Hindawi, vol. 2020, pages 1-13, August.
    6. Ndolane Sene & Guillermo Huerta Cuellar, 2021. "Study of a Fractional-Order Chaotic System Represented by the Caputo Operator," Complexity, Hindawi, vol. 2021, pages 1-20, June.
    7. Kuate, Paul Didier Kamdem & Tchendjeu, Achille Ecladore Tchahou & Fotsin, Hilaire, 2020. "A modified Rössler prototype-4 system based on Chua’s diode nonlinearity : Dynamics, multistability, multiscroll generation and FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    8. Janarthanan Ramadoss & Sajedeh Aghababaei & Fatemeh Parastesh & Karthikeyan Rajagopal & Sajad Jafari & Iqtadar Hussain & Guillermo Huerta Cuellar, 2021. "Chimera State in the Network of Fractional-Order FitzHugh–Nagumo Neurons," Complexity, Hindawi, vol. 2021, pages 1-9, June.
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    Cited by:

    1. N. C. Pati, 2023. "Bifurcations and multistability in a physically extended Lorenz system for rotating convection," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(8), pages 1-15, August.
    2. Cheng, Guanghui & Li, Dan & Yao, Yuangen & Gui, Rong, 2023. "Multi-scroll chaotic attractors with multi-wing via oscillatory potential wells," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Wang, Ning & Cui, Mengkai & Yu, Xihong & Shan, Yufan & Xu, Quan, 2023. "Generating multi-folded hidden Chua’s attractors: Two-case study," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    4. Peng, Hongxin & Ji’e, Musha & Du, Xinyu & Duan, Shukai & Wang, Lidan, 2023. "Design of pseudorandom number generator based on a controllable multi-double-scroll chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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