Dynamics of a ring of three fractional-order Duffing oscillators

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

Chaos, Solitons & Fractals, 2022, vol. 155, issue C

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.

Keywords: Duffing oscillator; Unidirectional coupling; Fractional-order differential equations; Multistability; Gründwall–Letnikov derivative (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921011012

DOI: 10.1016/j.chaos.2021.111747

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