Synchronization in systems with bimodal dynamics

Considering a prototypic model of a bimodal oscillator we investigate the synchronization of the internal time scales for a system with interacting fast and slow oscillatory modes. Particular emphasis is given to the transition between mode-locked and mode-unlocked chaos. It is shown that this transition involves a homoclinic bifurcation in which the synchronized chaotic attractor loses its band structure. For two coupled bimodal oscillators we illustrate the presence of separate synchronization regions for the fast and the slow modes. The dependence of these regions on the mismatch and coupling parameters is studied.