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On symmetric and asymmetric Van der Pol-Duffing oscillators

Author

Listed:
  • Vinícius Wiggers

    (Departamento de Física, Universidade do Estado de Santa Catarina)

  • Paulo C. Rech

    (Departamento de Física, Universidade do Estado de Santa Catarina)

Abstract

We investigate numerically the dynamics of both symmetric and asymmetric Van der Pol-Duffing oscillators driven by a periodic force F(t) = f cosωt. Each system is modeled by a different second order nonautonomous nonlinear ordinary differential equation controlled by five parameters. Our investigation takes into account the (ω, f) parameter-space in the two systems, keeping the other three parameters fixed. We verify the existence of parameter regions for which the corresponding trajectories in the phase-space are periodic, quasiperiodic, and chaotic, for the symmetric case. In the asymmetric case we verify the existence only of periodic and chaotic regions in the (ω, f) parameter-space. Finally, we also investigate the organization of the dynamics in the two systems, identifying Fibonacci and period-adding sequences of periodic structures.

Suggested Citation

  • Vinícius Wiggers & Paulo C. Rech, 2018. "On symmetric and asymmetric Van der Pol-Duffing oscillators," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(7), pages 1-6, July.
    • Handle: RePEc:spr:eurphb:v:91:y:2018:i:7:d:10.1140_epjb_e2018-90295-1
    DOI: 10.1140/epjb/e2018-90295-1
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    Cited by:

    1. Jianbin He & Jianping Cai, 2019. "Design of a New Chaotic System Based on Van Der Pol Oscillator and Its Encryption Application," Mathematics, MDPI, vol. 7(8), pages 1-12, August.
    2. Ramadoss, Janarthanan & Kengne, Jacques & Tanekou, Sosthene Tsamene & Rajagopal, Karthikeyan & Kenmoe, Germaine Djuidje, 2022. "Reversal of period doubling, multistability and symmetry breaking aspects for a system composed of a van der pol oscillator coupled to a duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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    Keywords

    Statistical and Nonlinear Physics;

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