Path-dependent Dynamics Induced by Rewiring Networks of Kuramoto Oscillators with Inertia

In networks of coupled oscillators, it is of wide interest to understand how interaction topology affects synchronization. Many studies have gained key insights into this question by studying the classic Kuramoto oscillator model on static networks. However, new questions arise when network structure is time-varying or when the oscillator system is multistable, which can occur by adding an inertial term to the Kuramoto model. While the consequences of evolving topology and multistability have been examined separately, real-world systems such as the brain may exhibit these properties simultaneously. This motivates investigation into how rewiring of network connectivity affects synchronization in systems with multistability, where different paths of network evolution may differentially impact collective behavior. To this end, we study the effects of evolving network topology on coupled Kuramoto oscillators with inertia. We find that certain fixed-density rewiring schemes induce significant changes to the level of global synchrony, and that these changes are robust to a wide range of network perturbations. Our findings suggest that the specific progression of network topology can play a considerable role in modulating the collective behavior of systems evolving on complex networks.