Driven synchronization in random networks of oscillators

TL;DR

This paper investigates how external driving influences synchronization in random networks of oscillators, revealing complex behaviors like bifurcations and bistability that depend on network topology.

Contribution

It introduces an analysis of driven synchronization in complex networks, highlighting the effects of network structure on dynamical states and transitions, including bifurcations and singularities.

Findings

Heterogeneous and homogeneous networks exhibit different bifurcation patterns.

Weak coupling regions show a Takens-Bogdanov-Cusp singularity.

Network topology significantly influences driven synchronization behaviors.

Abstract

Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns affect the types of behavior that it can produce. Thus far, modeling efforts have focused on the tendency of networks of oscillators to mutually synchronize themselves, with less emphasis on the effects of external driving. In this work we discuss the interplay between mutual and driven synchronization in networks of phase oscillators of the Kuramoto type, and explore how the structure and emergence of such states depends on the underlying network topology for simple random networks with a given degree distribution. We find a variety of interesting dynamical behaviors, including bifurcations and bistability patterns that are qualitatively different for heterogeneous and homogeneous networks, and which are separated by a Takens-Bogdanov-Cusp singularity in the parameter region where the coupling strength between oscillators is weak. Our analysis is connected to the underlying dynamics of oscillator clusters for important states and transitions.