Phase coalescence in a population of heterogeneous Kuramoto oscillators.

Phase coalescence (PC) is an emerging phenomenon in an ensemble of oscillators that manifests itself as a spontaneous rise in the order parameter. This increment in the order parameter is due to the overlaying of oscillator phases to a pre-existing system state. In the current work, we present a comprehensive analysis of the phenomenon of phase coalescence observed in a population of Kuramoto phase oscillators. The given population is divided into responsive and non-responsive oscillators depending on the position of the phases of the oscillators. The responsive set of oscillators is then reset by a pulse perturbation. This resetting leads to a temporary rise in a macroscopic observable, namely, order parameter. The provoked rise thus induced in the order parameter is followed by unprovoked increments separated by a constant time τ