Related papers: Synchronizing pulse-coupled oscillators by constra…
Networks of coupled nonlinear oscillators have been used to model circadian rhythms, flashing fireflies, Josephson junction arrays, high-voltage electric grids, and many other kinds of self-organizing systems. Recently, several authors have…
The phase-resetting curve (PRC) describes the response of a neural oscillator to small perturbations in membrane potential. Its usefulness for predicting the dynamics of weakly coupled deterministic networks has been well characterized.…
We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that…
A long-standing expectation is that two repulsively coupled oscillators tend to oscillate in opposite directions. It has been difficult to achieve complete synchrony in coupled identical oscillators with purely repulsive coupling. Here, we…
The asymptotic phase $\theta$ of an initial point $x$ in the stable manifold of a limit cycle identifies the phase of the point on the limit cycle to which the flow $\phi_t(x)$ converges as $t\to\infty$. The infinitesimal phase response…
In this paper, we consider the synchronization of heterogeneous pulse-coupled oscillators (PCOs), where some of the oscillators might be faulty or malicious. The oscillators interact through identical pulses at discrete instants and evolve…
We consider a network of identical pulse-coupled oscillators with delay and all-to-all coupling. We demonstrate that the discontinuous nature of the dynamics induces the appearance of isochronous regions---subsets of the phase space filled…
The phase sensitivity curve or phase response curve (PRC) quantifies the oscillator's reaction to stimulation at a specific phase and is a primary characteristic of a self-sustained oscillatory unit. Knowledge of this curve yields a phase…
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…
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…
It is shown that globally-coupled oscillators with pulse interaction can synchronize under broader conditions than widely believed from a theorem of Mirollo \& Strogatz \cite{MirolloII}. This behavior is stable against frozen disorder.…
We propose a population model for $\delta$-pulse-coupled oscillators with sparse connectivity. The model is given as an evolution equation for the phase density which take the form of a partial differential equation with a non-local term.…
We prove that a group of injection-locked oscillators, each modelled using a nonlinear phase macromodel, responds as a single oscillator to small external perturbations. More precisely, we show that any group of injection-locked oscillators…
We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the…
The emergence of collective synchronization was reproduced long ago by Winfree in a classical model consisting of an ensemble of pulse-coupled phase oscillators. By means of the Ott-Antonsen ansatz, we derive an exact low-dimensional…
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 theoretically investigate collective phase synchronization between interacting groups of globally coupled noisy identical phase oscillators exhibiting macroscopic rhythms. Using the phase reduction method, we derive coupled collective…
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…
We assess the power consumption of network synchronisation protocols, particularly the energy required to synchronise all nodes across a network. We use the widely adopted approach of bio-inspired, pulse-coupled oscillators to achieve…
Oscillators coupled in a network can synchronize with each other to yield a coherent population rhythm. If multiple such networks are coupled together, the question arises whether these rhythms will synchronize. We investigate the impact of…