Effect of periodic parametric excitation on an ensemble of force-coupled self-oscillators

We report the synchronization behavior in a one-dimensional chain of identical limit cycle oscillators coupled to a mass-spring load via a force relation. We consider the effect of periodic parametric modulation on the final synchronization states of the system. Two types of external parametric excitations are investigated numerically: periodic modulation of the stiffness of the inertial oscillator and periodic excitation of the frequency of the self-oscillatory element. We show that the synchronization scenarios are ruled not only by the choice of parameters of the excitation force but depend on the initial collective state in the ensemble. We give detailed analysis of entrainment behavior for initially homogeneous and inhomogeneous states. Among other results, we describe a regime of partial synchronization. This regime is characterized by the frequency of collective oscillation being entrained to the stimulation frequency but different from the average individual oscillators frequency.