Related papers: Cluster and group synchronization in delay-coupled…

We study the synchronization of coupled maps on a variety of networks including regular one and two dimensional networks, scale free networks, small world networks, tree networks, and random networks. For small coupling strengths nodes show…

An outstanding problem in the study of networks of heterogeneous dynamical units concerns the development of rigorous methods to probe the stability of synchronous states when the differences between the units are not small. Here, we…

The stability analysis of synchronization patterns on generalized network structures is of immense importance nowadays. In this article, we scrutinize the stability of intralayer synchronous state in temporal multilayer hypernetworks, where…

Synchrony patterns characterize network states in which nodes organize into clusters based on their synchronized dynamics. The synchronized clusters may further exhibit either active or inactive states. The simultaneous invariance of active…

We consider a general model for a network of oscillators with time delayed, circulant coupling. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay…

Cluster synchronization in networks of coupled oscillators is the subject of broad interest from the scientific community, with applications ranging from neural to social and animal networks and technological systems. Most of these networks…

In networks of periodically firing spiking neurons that are interconnected with chemical synapses, we analyze cluster state, where an ensemble of neurons are subdivided into a few clusters, in each of which neurons exhibit perfect…

Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…

We study cluster synchronization in networks and show that the stability of all possible cluster synchronization patterns depends on a small set of Lyapunov exponents. Our approach can be applied to clusters corresponding to both orbital…

Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…

We derive a master stability function (MSF) for synchronization in networks of coupled dynamical systems with small but arbitrary parametric variations. Analogous to the MSF for identical systems, our generalized MSF simultaneously solves…

We present a technique to engineer solitary states by means of delayed links in a network of neural oscillators and in coupled chaotic maps. Solitary states are intriguing partial synchronization patterns, where a synchronized cluster…

We investigate the combined effects of distributed delay and the balance between excitatory and inhibitory nodes on the stability of synchronous oscillations in a network of coupled Stuart--Landau oscillators. To this end a network model is…

We investigate the connection between the dynamics of synchronization and the modularity on complex networks. Simulating the Kuramoto's model in complex networks we determine patterns of meta-stability and calculate the modularity of the…

We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the…

We study the impact of interaction of nodes in a layer of a multiplex network on the dynamical behavior and cluster synchronization of these nodes in other layers. We find that nodes interactions in one layer affects the cluster…

We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. We focus on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone. Comparing the synchronization properties…

We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on…

We review some recent work on the synchronization of coupled dynamical systems on a variety of networks. When nodes show synchronized behaviour, two interesting phenomena can be observed. First, there are some nodes of the floating type…

We investigate the stability of synchronization in networks of dynamical systems with strongly delayed connections. We obtain strict conditions for synchronization of periodic and equilibrium solutions. In particular, we show the existence…