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Dynamics of a ring of three fractional-order Duffing oscillators

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  • Barba-Franco, J.J.
  • Gallegos, A.
  • Jaimes-Reátegui, R.
  • Pisarchik, A.N.

Abstract

We investigate the dynamics of three ring-coupled double-well Duffing oscillators modelled by fractional-order differential equations. The analysis of time series, Fourier spectra, phase portraits, Poincaré sections, and Lyapunov exponents using the fractional order and the coupling strength as control parameters, shows that the dynamics of such system is much richer than that of the system with integer order. We demonstrate the appearance of multistability and a rotating wave when either the fractional derivative index or the coupling strength is increased, on the route from a stable steady-state regime to hyperchaos through a Hopf bifurcation and a cascade of torus bifurcations.

Suggested Citation

  • Barba-Franco, J.J. & Gallegos, A. & Jaimes-Reátegui, R. & Pisarchik, A.N., 2022. "Dynamics of a ring of three fractional-order Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921011012
    DOI: 10.1016/j.chaos.2021.111747
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    References listed on IDEAS

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    1. L. Borkowski & A. Stefanski, 2015. "FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, December.
    2. Ge, Zheng-Ming & Ou, Chan-Yi, 2007. "Chaos in a fractional order modified Duffing system," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 262-291.
    3. Chandrakala Meena & Pranay Deep Rungta & Sudeshna Sinha, 2020. "Resilience of networks of multi-stable chaotic systems to targetted attacks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(11), pages 1-9, November.
    4. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou, 2007. "Chaotic dynamics of the fractionally damped Duffing equation," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1459-1468.
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