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Populations of flashing fireflies, claps of applauding audience, cells of cardiac and circadian pacemakers reach synchrony via event-triggered interactions, referred to as pulse couplings. Synchronization via pulse coupling is widely used…
In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be…
In this article we study the behavior of globally coupled assemblies of a large number of Integrate and Fire oscillators with excitatory pulse-like interactions. On some simple models we show that the additive effects of pulses on the state…
Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a…
Understanding complex systems which exhibit desynchronization as an emergent property should have important implications, particularly in treating neurological disorders and designing efficient communication networks. Here were demonstrate…
We analyze the emergence of synchronization in a population of moving integrate-and-fire oscillators. Oscillators, while moving on a plane, interact with their nearest neighbor upon firing time. We discover a non-monotonic dependence of the…
In this article I investigate the novel synchronization behaviors of evolving pulse-coupled oscillator networks. Unlike previous models, the time-varying mechanism is inspired by neural network development, where seldom used links die out…
We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators…
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…
A simple system composed of electronic oscillators capable of emitting and detecting light-pulses is studied. The oscillators are biologically inspired, their behavior is designed for keeping a desired light intensity, W, in the system.…
Collective behavior of pulse-coupled oscillators has been investigated widely. As an example of pulse-coupled networks, fireflies display many kinds of flashing patterns. Mirollo and Strogatz (1990) proposed a pulse-coupled oscillator model…
An electronic implementation referring to fireflies ensembles flashing in synchrony in a self-organization mode, shows the details of the phase-locking mechanism and how the phases between the electronic oscillators are related to their…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean…
We study synchronization dynamics of a population of pulse-coupled oscillators. In particular, we focus our attention in the interplay between networks topological disorder and its synchronization features. Firstly, we analyze…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…
The mechanism of phase synchronization between uncoupled limit-cycle oscillators induced by common external impulsive forcing is analyzed. By reducing the dynamics of the oscillator to a random phase map, it is shown that phase…
We develop a formalism to analyze the behaviour of pulse--coupled identical phase oscillators with a specific attention devoted to the onset of partial synchronization. The method, which allows describing the dynamics both at the…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
We explore systems of pulse-coupled oscillators beyond the mean-field limit [R.E. Mirollo and S.H. Strogatz, {SIAM J. Appl. Math.} {\bf 50}, 1645 (1990)] by means of a manageable description which leads to a great simplification of the…