Dynamics of a ring of three fractional-order Duffing oscillators

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, Poincare sec-tions, 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.(c) 2021 Elsevier Ltd. All rights reserved.