Robust Almost Global Splay State Stabilization of Pulse Coupled Oscillators

Stability of the splay state in pulse-coupled networks.

The stability of the dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of globally coupled leaky integrate-and-fire neurons. This is done by reducing the set of differential equations to a map that is investigated in the limit of large network size. We show that the stability of the splay state depends crucially on the ratio between the pulse width ...

Synchronization of finite-state pulse-coupled oscillators

We propose a simple cellular automata model for discrete-time pulse-coupled oscillators and study its network behavior. Given a finite simple graph and an integer n ≥ 3, each vertex will be considered as an identical oscillator of period n with the following weak coupling along the edges: any oscillator with a particular "blinking" state will postpone the update of its neighbors whose states ar...

Almost Global Synchronization of Symmetric Kuramoto Coupled Oscillators

Global analysis of pulse-coupled oscillators: discrete and continuous models

The Peskin model [1] is a simple but seminal model to study networks of interacting agents, such as pacemaker cells of the heart or neurons. Each agent corresponds to an oscillator whose state variable xi evolves according to the dynamics ẋi = F(xi) > 0 between two threshold values. Upon reaching the upper threshold, the state is reset to the lower threshold — the oscillator is said to fire. Th...

Global Synchronization of Pulse-Coupled Oscillators Interacting on Cycle Graphs

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 networks that are more general than all-to-all connected is still unavailable. In this paper we address global synchronization of PCO networks described by cycle gr...