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Coupled oscillators, even identical ones, display a wide range of behaviours, among them synchrony and incoherence. The 2002 discovery of so-called chimera states, states of coexisting synchronized and unsynchronized oscillators, provided a…
The internal state of a cell in a coupled cell network is often described by an element of a vector space. Synchrony or anti-synchrony occurs when some of the cells are in the same or the opposite state. Subspaces of the state space…
We show that dynamical clustering, where a system segregates into distinguishable subsets of synchronized elements, and chimera states, where differentiated subsets of synchronized and desynchronized elements coexist, can emerge in networks…
We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…
The presence of synchronized clusters in neuron networks is a hallmark of information transmission and processing. The methods commonly used to study cluster synchronization in networks of coupled oscillators ground on simplifying…
We consider the coupling between two networks, each having N nodes whose individual dynamics is modeled by a two-state master equation. The intra-network interactions are all to all, whereas the inter-network interactions involve only a…
In the light of the recently proposed scenario of asymmetry-induced synchronization (AISync), in which dynamical uniformity and consensus in a distributed system would demand certain asymmetries in the underlying network, we investigate…
Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the…
In a recent study of chaos synchronization in symmetric complex networks [Pecora \textit{et al}., Nat. Commun. {\bf 5}, 4079 (2014)], it is found that stable synchronous clusters may coexist with many non-synchronous nodes in the…
Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by…
We consider weighted coupled cell networks, that is networks where the interactions between any two cells have an associated weight that is a real valued number. Weighted networks are ubiquitous in real-world applications. We consider a…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
We study the phase synchronization and cluster formation in coupled maps on different networks. We identify two different mechanisms of cluster formation; (a) {\it Self-organized} phase synchronization which leads to clusters with dominant…
We study a system of coupled pendula with diffusive interactions, which could depend both on positions and on momenta. The coupling structure is defined by an undirected network, while the dynamic equations are derived from a Hamiltonian;…
We consider synchronization of chaotic systems coupled indirectly through a common environmnet where the environment has an intrinsic dynmics of its own modulated via feedback from the systems. We find that a rich vareity of synchronization…
Synchronization of coupled oscillators is a fundamental process in both natural and artificial networks. While much work has investigated the asymptotic stability of the synchronous solution, the fundamental question of the transient…
Network interactions that are nonlinear in the state of more than two nodes - also known as higher-order interactions - can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to…
Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
We demonstrate the mechanisms of emergence and the link between two types of symmetry-broken states, the unbalanced periodic two-cluster states and solitary states, in coupled excitable systems with prevalent repulsive interactions.…