Related papers: Synchronization of Pulse-Coupled Oscillators and C…
Clock synchronization is a widely discussed topic in the engineering literature. Ensuring that individual clocks are closely aligned is important in network systems, since the correct timing of various events in a network is usually…
Driven by increased applications in biological networks and wireless sensor networks, synchronization of pulse-coupled oscillators (PCOs) has gained increased popularity. However, most existing results address the local synchronization of…
Synchronization by exchange of pulses is a widespread phenomenon, observed in flashing fireflies, applauding audiences and the neuronal network of the brain. Hitherto the focus has been on integrate-and-fire oscillators. Here we consider…
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 introduce a system of pulse coupled oscillators that can change both their phases and frequencies; and prove that when there is a separation of time scales between phase and frequency adjustment the system converges to exact synchrony on…
By spreading phases on the unit circle, desynchronization algorithm is a powerful tool to achieve round-robin scheduling, which is crucial in applications as diverse as media access control of communication networks, realization of…
Consider a distributed network on a finite simple graph $G=(V,E)$ with diameter $d$ and maximum degree $\Delta$, where each node has a phase oscillator revolving on $S^{1}=\mathbb{R}/\mathbb{Z}$ with unit speed. Pulse-coupling is a class of…
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…
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 show that a large class of pulse coupled oscillators converge with high probability from random initial conditions on a large class of graphs with time delays. Our analysis combines previous local convergence results, probabilistic…
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…
We show that for pulse coupled oscillators a class of phase response curves with both excitation and inhibition exhibit robust convergence to synchrony on arbitrary aperiodic connected graphs with delays. We describe the basins of…
This paper addresses the synchronization rate of weakly connected pulse-coupled oscillators (PCOs). We prove that besides coupling strength, the phase response function is also a determinant of synchronization rate. Inspired by the result,…
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…
Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a…
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…
The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator…
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…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
The precision of synchronization algorithms based on the theory of pulse-coupled oscillators is evaluated on FPGA-based radios for the first time. Measurements show that such algorithms can reach precision in the low microsecond range when…