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We study synchronization in delay-coupled oscillator networks, using a master stability function approach. Within a generic model of Stuart-Landau oscillators (normal form of super- or subcritical Hopf bifurcation) we derive analytical…
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.…
Delayed interactions are a common property of coupled natural systems and therefore arise in a variety of different applications. For instance, signals in neural or laser networks propagate at finite speed giving rise to delayed…
We investigate solitary states in a two-layer multiplex network of FitzHugh-Nagumo neurons in the oscillatory regime. We demonstrate how solitary states can be induced in a multiplex network consisting of two non-identical layers. More…
We discuss the desynchronization transition in networks of globally coupled identical oscillators with attractive and repulsive interactions. We show that, if attractive and repulsive groups act in antiphase or close to that, a solitary…
Lag synchronization is a basic phenomenon in mismatched coupled systems, delay coupled systems and time-delayed systems. It is characterized by a lag configuration that establishes a unique time shift between all the state variables of the…
We investigate the effects of transmission delays on the formation of temporally ordered states in networks of non-identical R\"ossler oscillators, having SWN topology. We show that incorporation of two different types of delay, length…
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…
Chimera referring to a coexistence of coherent and incoherent states, is traditionally very difficult to control due to its peculiar nature. Here, we provide a recipe to construct chimera states in the multiplex networks with the aid of…
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…
Many time-evolving systems in nature, society and technology leave traces of the interactions within them. These interactions form temporal networks that reflect the states of the systems. In this work, we pursue a coarse-grained…
We study the constructive role of noises in a Lorenz system with functional delay. The effect of delay can change the dynamics of the system to a chaotic one from its steady state. Induced synchronization with white and colored (red and…
In-phase synchronization is a special case of synchronous behavior when coupled oscillators have the same phases for any time moments. Such behavior appears naturally for nearly identical coupled limit-cycle oscillators when the coupling…
Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks allow for their explicit analysis.…
We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory…
Communication delays and multiplexing are ubiquitous features of real-world networked systems. We here introduce a simple model where these two features are simultaneously present, and report the rich phe- nomenology which is actually due…
A novel regime of synchronization, called remote synchronization, where the peripheral nodes form a phase synchronized cluster not including the hub, was recently observed in star motifs. We show the existence of a more general dynamical…
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,…
The chaotic spike train of a homoclinic dynamical system is self-synchronized by re-inserting a small fraction of the delayed output. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long…
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…