All beauty, richness and harmony in the emergent dynamics of a complex system largely
depend on the specific way in which its elementary components interact. The last twenty-five …

Networks in nature have complex interactions among agents. One significant phenomenon
induced by interactions is synchronization of coupled agents, and the interactive network …

Hypergraphs have emerged as a powerful modeling framework to represent systems with
multiway interactions, that is systems where interactions may involve an arbitrary number of …

Full synchronization of dynamical elements coupled via hypergraphs can be analyzed with
the hypergraph projection onto dyadic matrices, but this is not sufficient for analyzing cluster …

Chimera dynamics, an intriguing phenomenon of coupled oscillators, is characterized by the
coexistence of coherence and incoherence, arising from a symmetry-breaking mechanism …

Coupled oscillator networks provide mathematical models for interacting periodic processes.
If the coupling is weak, phase reduction—the reduction of the dynamics onto an invariant …

In this review we survey the literature on mean-field coupled maps. We start with the early
works from the physics literature, arriving to some recent results from ergodic theory studying …

Many science phenomena are described as interacting particle systems (IPS). The mean
field limit (MFL) of large all-to-all coupled deterministic IPS is given by the solution of a PDE …

We introduce a method to identify phase equations that include-body interactions for general
coupled oscillators valid far beyond the weak coupling approximation. This strategy is an …

Many science phenomena are modelled as interacting particle systems (IPS) coupled on
static networks. In reality, network connections are far more dynamic. Connections among …