The complexity of many biological, social and technological systems stems from the richness
of the interactions among their units. Over the past decades, a variety of complex systems …

Network-based modeling of complex systems and data using the language of graphs has
become an essential topic across a range of different disciplines. Arguably, this graph-based …

Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity
occurs, for instance, in active matter,,,,–, non-equilibrium systems,–, networks of neurons …

Synchronization of an ensemble of oscillators is an emergent phenomenon present in
several complex systems, ranging from social and physical to biological and technological …

A chimera state is a spatio-temporal pattern in a network of identical coupled oscillators in
which synchronous and asynchronous oscillation coexist. This state of broken symmetry …

Many biological and neural systems can be seen as networks of interacting periodic
processes. Importantly, their functionality, ie, whether these networks can perform their …

Percolation and synchronization are two phase transitions that have been extensively
studied since already long ago. A classic result is that, in the vast majority of cases, these …

The emergence of large-scale connectivity and synchronization are crucial to the structure,
function and failure of many complex socio-technical networks. Thus, there is great interest …

We show that many coupled oscillator array configurations considered in the literature can
be put into a simple form so that determining the stability of the synchronous state can be …

It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators
display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear …