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We study the dynamical behavior of an ensemble of oscillators interacting through short range bidirectional pulses. The geometry is 1D with periodic boundary conditions. Our interest is twofold. To explore the conditions required to reach…
We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a Winner…
In this paper we study synchronized motions in complex networks in which there are distinct groups of nodes where the dynamical systems on each node within a group are the same but are different for nodes in different groups. Both…
Dissipative coupling is known to induce synchronization. Conversely it may be hypothesized that oscillators driven to synchronize may reduce power dissipation in their coupling. The latter scenario is realized in the human cardiorespiratory…
Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems.…
We investigate the transition to synchronization in a two-layer network with time-switching inter-layer links. We focus on the role of the number of inter-layer links and the time-scale of topological changes. Initially, we observe a smooth…
The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into…
The importance of pulse-coupled oscillators (PCOs) in biology and engineering has motivated research to understand basic properties of PCO networks. Despite the large body of work addressing PCOs, a global synchronization result for…
Synchronization is a hallmark of collective behavior that emerges when nonlinear systems interact, spanning scales from mechanical oscillators to planetary orbits. As a universal phenomenon it underpins the study of complex systems and has…
Experimental studies of synchronization properties on networks with controlled connection topology can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection…
We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we…
We consider a system of coupled oscillators with finite inertia and time-delayed interaction, and investigate the interplay between inertia and delay both analytically and numerically. The phase velocity of the system is examined; revealed…
We study the evolution of heterogeneous networks of oscillators subject to a state-dependent interconnection rule. We find that heterogeneity in the node dynamics is key in organizing the architecture of the functional emerging networks. We…
We study a network of coupled logistic maps whose interactions occur with a certain distribution of delay times. The local dynamics is chaotic in the absence of coupling and thus the network is a paradigm of a complex system. There are two…
We show that simultaneous synchronization between two delay-coupled oscillators can be achieved by relaying the dynamics via a third mediating element, which surprisingly lags behind the synchronized outer elements. The zero-lag…
This paper provides synchronization conditions for networks of nonlinear systems. The components of the network (referred to as "compartments'' in this paper) are made up of an identical interconnection of subsystems, each represented as an…
Many oscillator networks are multistable, meaning that different synchronization states are realized depending on the initial conditions. In this paper, we numerically analyze a ring network of phase oscillators, in which synchronous states…
We study synchronization of Kuramoto oscillators in strongly modular networks in which the structure of the network inside each community is averaged. We find that the dynamics of the interacting communities can be described as an ensemble…
We theoretically investigate collective phase synchronization between interacting groups of globally coupled noisy identical phase oscillators exhibiting macroscopic rhythms. Using the phase reduction method, we derive coupled collective…
We study the periodic forced response of a system of two limit cycle oscillators that interact with each other via a time delayed coupling. Detailed bifurcation diagrams in the parameter space of the forcing amplitude and forcing frequency…