ON PHASE SYNCHRONIZATION BY PERIODIC FORCE IN CHAOTIC OSCILLATORS WITH SADDLE EQUILIBRIA

Abstract

A periodic action onto a chaotic system can result in phase synchronization: Although the oscillations remain chaotic, their pace is prescribed by the rhythm of the force. We show how this adjustment of characteristic timescales to the period of the forcing is violated when, due to the presence of a saddle point in the autonomous attractor, the time intervals between returns onto a Poincaré plane are unbounded. In such a situation, the segments of a chaotic trajectory in which its phase follows the phase of the force, can alternate with short segments of phase-locking in ratios different from 1:1. This phenomenon is demonstrated for several nonlinear systems.