It is a fundamental challenge to understand how the function of a network is related to its
structural organization. Adaptive dynamical networks represent a broad class of systems that …

In this paper, we discuss recent progress in research of ensembles of mean field coupled
oscillators. Without an ambition to present a comprehensive review, we outline most …

The dynamical systems found in nature are rarely isolated. Instead they interact and
influence each other. The coupling functions that connect them contain detailed information …

Phase synchronizations in models of coupled oscillators such as the Kuramoto model have
been widely studied with pairwise couplings on arbitrary topologies, showing many …

Critical transitions are observed in many complex systems. This includes the onset of
synchronization in a network of coupled oscillators or the emergence of an epidemic state …

From critical infrastructure to physiology and the human brain, complex systems rarely occur
in isolation. Instead, the functioning of nodes in one system often promotes or suppresses …

We study excitation and suppression of chimera states in an ensemble of nonlocally coupled
oscillators arranged in a framework of multiplex network. We consider the homogeneous …

Large communities of biological oscillators show a prevalent tendency to self-organize in
time. This cooperative phenomenon inspired Winfree to formulate a mathematical model that …

We design and analyze the dynamics of a large network of theta neurons, which are
idealized type I neurons. The network is heterogeneous in that it includes both inherently …

Swarmalators are phase oscillators that cluster in space, like fireflies flashing in a swarm to
attract mates. Interactions between particles, which tend to synchronize their phases and …