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Coexisting attractors and basins of attraction of an extended forced Duffing oscillator

Author

Listed:
  • Isabelle L. Soares

    (Universidade do Estado de Santa Catarina)

  • Marcelo F. Krol

    (Universidade do Estado de Santa Catarina)

  • Paulo C. Rech

    (Universidade do Estado de Santa Catarina)

Abstract

In this paper we investigate the dynamics of an extended form of a symmetric Duffing oscillator driven by a periodic force $$F(t)=A \cos \omega t$$ F ( t ) = A cos ω t . The system is modeled by a second-order nonautonomous nonlinear ordinary differential equation, and controlled by seven parameters. Our study takes into account the $$(\omega ,A)$$ ( ω , A ) parameter plane of the system, consequently keeping the other five parameters fixed. We verify the existence of parameter regions for which the corresponding trajectories in the phase-space are periodic or chaotic, delimiting therefore such regions in the $$(\omega ,A)$$ ( ω , A ) parameter plane. Finally, we use this same $$(\omega ,A)$$ ( ω , A ) parameter plane to locate multistability regions. Examples of basins of attraction of coexisting periodic and chaotic attractors are presented, as well as the related attractors. Graphic Abstract Projections of basins of attraction onto the xy plane of initial conditions for an extended forced Duffing oscillator. Black (Red) regions are related to a periodic (chaotic) attractor basin of attraction.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurphb:v:97:y:2024:i:6:d:10.1140_epjb_s10051-024-00709-0
    DOI: 10.1140/epjb/s10051-024-00709-0
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    References listed on IDEAS

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    1. Sk, Nazmul & Mondal, Bapin & Thirthar, Ashraf Adnan & Alqudah, Manar A. & Abdeljawad, Thabet, 2023. "Bistability and tristability in a deterministic prey–predator model: Transitions and emergent patterns in its stochastic counterpart," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Han, Xiujing & Bi, Qinsheng, 2023. "Sliding fast–slow dynamics in the slowly forced Duffing system with frequency switching," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Cheng, Haihui & Meng, Xinzhu & Hayat, Tasawar & Hobiny, Aatef, 2023. "Multistability and bifurcation analysis for a three-strategy game system with public goods feedback and discrete delays," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
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    5. Vinícius Wiggers & Paulo C. Rech, 2022. "On the dynamics of a Van der Pol–Duffing snap system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(2), pages 1-6, February.
    6. Rech, Paulo C., 2022. "Self-excited and hidden attractors in a multistable jerk system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    7. Muhammad Ahsar Karim & Agus Yodi Gunawan, 2020. "Parameter Estimations of Fuzzy Forced Duffing Equation: Numerical Performances by the Extended Runge-Kutta Method," Abstract and Applied Analysis, Hindawi, vol. 2020, pages 1-9, April.
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