Rhythmic behavior represents one of the most striking and ubiquitous manifestations of
functional evolution for a wide class of natural and man-made systems. The emergence of …

We present a systematic approach to reveal the correspondence between time delay
dynamics and networks of coupled oscillators. After early demonstrations of the usefulness …

Interactions and emergent processes are essential for research on complex systems
involving many components. Most studies focus solely on pairwise interactions and ignore …

Behavioral homogeneity is often critical for the functioning of network systems of interacting
entities. In power grids, whose stable operation requires generator frequencies to be …

A widely held assumption on network dynamics is that similar components are more likely to
exhibit similar behavior than dissimilar ones and that generic differences among them are …

Spontaneous symmetry breaking is central to our understanding of physics and explains
many natural phenomena, from cosmic scales to subatomic particles. Its use for applications …

Exploring the collective behavior of interacting entities is of great interest and importance.
Rather than focusing on static and uniform connections, we examine the co-evolution of …

Repulsive oscillator networks can exhibit multiple cooperative rhythms, including chimera
and cluster splay states. Yet, understanding which rhythm prevails remains challenging …

Symmetries are ubiquitous in network systems and have profound impacts on the
observable dynamics. At the most fundamental level, many synchronization patterns are …

The study of synchronization of coupled systems is currently undergoing a major surge
fueled by recent discoveries of new forms of collective dynamics and the development of …