Path-dependent dynamics induced by rewiring networks of inertial oscillators.

In networks of coupled oscillators, it is of 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 the network structure is time varying or when the oscillator system is multistable, the latter of which can occur when an inertial term is added to the Kuramoto model. While the consequences of evolving topology and multistability on collective behavior have been examined separately, real-world systems such as gene regulatory networks and the brain may exhibit these properties simultaneously. It is thus relevant to ask how time-varying network connectivity impacts synchronization in systems that can exhibit multistability. To address this question, we study how the dynamics of coupled Kuramoto oscillators with inertia are affected when the topology of the underlying network changes in time. We show that hysteretic synchronization behavior in networks of coupled inertial oscillators can be driven by changes in connection topology alone. Moreover, we find that certain fixed-density rewiring schemes induce significant changes to the level of global synchrony that remain even after the network returns to its initial configuration, and we show that these changes are robust to a wide range of network perturbations. Our findings highlight that the specific progression of network topology over time, in addition to its initial or final static structure, can play a considerable role in modulating the collective behavior of systems evolving on complex networks.