Related papers: Synchronizing pulse-coupled oscillators by constra…
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…
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…
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…
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 present an approach for reconstructing networks of pulse-coupled neuron-like oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases…
Many real oscillators are coupled to other oscillators and the coupling can affect the response of the oscillators to stimuli. We investigate phase response curves (PRCs) of coupled oscillators. The PRCs for two weakly coupled phase-locked…
Pulse-coupled spiking neural networks are a powerful tool to gain mechanistic insights into how neurons self-organize to produce coherent collective behavior. These networks use simple spiking neuron models, such as the $\theta$-neuron or…
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 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…
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…
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…
For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via…
Phase response curve (PRC) is an extremely useful tool for studying the response of oscillatory systems, e.g. neurons, to sparse or weak stimulation. Here we develop a framework for studying the response to a series of pulses which are…
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…
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 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…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
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…
Synchronized neural spiking is associated with many cognitive functions and thus, merits study for its own sake. The analysis of neural synchronization naturally leads to the study of repetitive spiking and consequently to the analysis of…
We study the synchronization behavior of a noisy network in which each system is driven by two sources of state-dependent noise: (1) an intrinsic noise which is common among all systems and can be generated by the environment or any…