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Homoclinic bifurcation and chaos in Duffing oscillator driven by an amplitude-modulated force

Author

Listed:
  • Ravichandran, V.
  • Chinnathambi, V.
  • Rajasekar, S.

Abstract

The homoclinic bifurcation and transition from regular to asymptotic chaos in Duffing oscillator subjected to an amplitude modulated force is studied both analytically and numerically. Applying the Melnikov analytical method, the threshold condition for the occurrence of horseshoe chaos is obtained. Melnikov threshold curves are drawn in different external parameters space. Analytical predictions are demonstrated through direct numerical simulations. Parametric regimes where suppression of horseshoe chaos occurs are predicted. Period doubling route to chaos, intermittency route to chaos and quasiperiodic route to chaos are found to occur due to the amplitude-modulated force. Numerical investigations including computation of stable and unstable manifolds of saddle, maximal Lyapunov exponent, Poincaré map and bifurcation diagrams are used to detect homoclinic bifurcation and chaos.

Suggested Citation

  • Ravichandran, V. & Chinnathambi, V. & Rajasekar, S., 2007. "Homoclinic bifurcation and chaos in Duffing oscillator driven by an amplitude-modulated force," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 223-236.
    • Handle: RePEc:eee:phsmap:v:376:y:2007:i:c:p:223-236
    DOI: 10.1016/j.physa.2006.11.003
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    Cited by:

    1. Miwadinou, C.H. & Monwanou, A.V. & Hinvi, L.A. & Chabi Orou, J.B., 2018. "Effect of amplitude modulated signal on chaotic motions in a mixed Rayleigh–Liénard oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 89-101.
    2. Balamurali, Ramakrishnan & Kamdjeu Kengne, Leandre & Rajagopal, Karthikeyan & Kengne, Jacques, 2022. "Coupled non-oscillatory Duffing oscillators: Multistability, multiscroll chaos generation and circuit realization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    3. Zhang, Zhonghua & Peng, Jigen & Zhang, Juan, 2009. "Melnikov method to a bacteria-immunity model with bacterial quorum sensing mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 414-420.

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