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Patterns and stability of coupled multi-stable nonlinear oscillators

Author

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  • Bel, G.
  • Alexandrov, B.S.
  • Bishop, A.R.
  • Rasmussen, K.Ø.

Abstract

Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and stability of coupled driven-damped Helmholtz–Duffing oscillators in bi-stability regimes. We find that despite the fact that the system parameters and the driving force are identical, the stability of the two states to spatially non-uniform perturbations is very different. Moreover, the final stable states, resulting from these spatial perturbations, are not solely dictated by the wavelength of the perturbing mode and take different spatial configurations in terms of the coupled oscillator phases.

Suggested Citation

  • Bel, G. & Alexandrov, B.S. & Bishop, A.R. & Rasmussen, K.Ø., 2023. "Patterns and stability of coupled multi-stable nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s096007792201178x
    DOI: 10.1016/j.chaos.2022.112999
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    References listed on IDEAS

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    1. Musielak, D.E. & Musielak, Z.E. & Benner, J.W., 2005. "Chaos and routes to chaos in coupled Duffing oscillators with multiple degrees of freedom," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 907-922.
    2. Rajasekar, S. & Valsakumar, M.C. & Raj, S.Paul, 1998. "Noise-induced jumps in two coupled Duffing oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 417-434.
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    Cited by:

    1. Remus-Daniel Ene & Nicolina Pop, 2023. "Optimal Homotopy Asymptotic Method for an Anharmonic Oscillator: Application to the Chen System," Mathematics, MDPI, vol. 11(5), pages 1-14, February.
    2. Shen, Yuan & Tian, Bo & Zhou, Tian-Yu & Cheng, Chong-Dong, 2023. "Multi-pole solitons in an inhomogeneous multi-component nonlinear optical medium," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).

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