Related papers: Isochronous Dynamics in Pulse Coupled Oscillator N…
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…
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 small network models for mutually delay-coupled systems which typically do not exhibit stable isochronally synchronized solutions. We show that for certain coupling architectures which involve delayed self feedback to the nodes,…
We consider an ensemble of globally coupled phase oscillators whose interaction is transmitted at finite speed. This introduces time delays, which make the spatial coordinates relevant in spite of the infinite range of the interaction. We…
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…
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…
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…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…
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…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
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…
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…
An oscillator is called isochronous if all motions have a common period. When the system is forced by a time-dependent perturbation with the same period the dynamics may change and the phenomenon of resonance can appear. In this context,…
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…
We present and analyze deterministic complex networks of pulse-coupled oscillators that exhibits recurrent events comprised of an increase and a decline in synchrony. Events emerging from the networks may form an oscillatory behavior or may…
For networks of pulse-coupled oscillators with delayed excitatory coupling, we analyze the firing behaviors depending on coupling strength and transmission delay. The parameter space consisting of strength and delay is partitioned into two…
Effects of synchronization in a system of two coupled oscillators with time-delayed feedback are investigated. Phase space of a system with time delay is infinite-dimensional. Thus, the picture of synchronization in such systems acquires…
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…
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…
By means of numerical integration we investigate the coherent and incoherent phases in a generalized Kuramoto model of phase-coupled oscillators with distance-dependent delay. Preserving the topology of a complete graph, we arrange the…