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Effect of amplitude modulated signal on chaotic motions in a mixed Rayleigh–Liénard oscillator

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  • Miwadinou, C.H.
  • Monwanou, A.V.
  • Hinvi, L.A.
  • Chabi Orou, J.B.

Abstract

This paper addresses the issues of the control of chaotic motions in a mixed Rayleigh-Liénard oscillator by amplitude modulated excitation. The Melnikov method is used to analytically determine the domains boundaries where horseshoes chaos appears. The basin of attraction has been drawn to confirm the horseshoes chaos appearance domain. Routes to chaos are investigated through bifurcations structures, Lyapunov exponent, phase portraits and Poincaré section. The effects of control force on chaotic motions are strongly analyzed and the control efficiency is found where the cases of g=0 (unmodulated case), g ≠ 0 with Ω=ω and Ωω≠pq where p and q are simple positive integers are considered. Results of analytical investigations are validated and complemented by numerical simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:113:y:2018:i:c:p:89-101
    DOI: 10.1016/j.chaos.2018.05.021
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    References listed on IDEAS

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    1. Anague Tabejieu, L.M. & Nana Nbendjo, B.R. & Woafo, P., 2016. "On the dynamics of Rayleigh beams resting on fractional-order viscoelastic Pasternak foundations subjected to moving loads," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 39-47.
    2. 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.
    3. R. Yamapi & G. Filatrella & M. A. Aziz-Alaoui & H. G. Enjieu Kadji, 2014. "Modeling, Stability, Synchronization, and Chaos and Their Applications to Complex Systems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-2, February.
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    Cited by:

    1. Yue, Xiaole & Yu, Bei & Li, Yongge & Xu, Yong, 2022. "Dynamic response and bifurcation for Rayleigh-Liénard oscillator under multiplicative colored noise," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Miwadinou, C.H. & Olabodé, D.L. & Monwanou, A.V. & Enjieu Kadji, H.G. & Chabi Orou, J.B., 2023. "Nonlinear dynamics and passive control of GLYCOLYTIC oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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