FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions

Abstract EN

The dynamics of a ring of seven unidirectionally coupled nonlinear Duffing oscillators is studied.

We show that the FFT analysis presented in form of a bifurcation graph, that is, frequency distribution versus a control parameter, can provide a valuable and helpful complement to the corresponding typical bifurcation diagram and the course of Lyapunov exponents, especially in context of detailed identification of the observed attractors.

As an example, bifurcation analysis of routes to chaos via 2-frequency and 3-frequency quasiperiodicity is demonstrated.