Self-induced slow-fast dynamics and swept bifurcation diagrams in weakly desynchronized systems

In systems close to the state of phase synchronization, the fast timescale of oscillations interacts, with the slow timescale of the phase drift. As a result, "fast" dynamics is subjected to a slow modulation, due to which an autonomous system under fixed parameter value, can imitate repeated bifurcational transitions. We demonstrate the action of this general mechanism for a set of two coupled autonomous chaotic oscillators and for a chaotic system perturbed by a periodic external force. In both cases, the Poincare sections of phase portraits resemble bifurcation diagram of a logistic mapping with time-dependent parameter.