Related papers: Synchronizing pulse-coupled oscillators by constra…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…
Coupled parametric oscillators were recently employed as simulators of artificial Ising networks, with the potential to solve computationally hard minimization problems. We demonstrate a new dynamical regime within the simplest network -…
In this paper we propose a novel geometric method, based on singular perturbations, to approximate isochrones of relaxation oscillators and predict the qualitative shape of their (finite) phase response curve. This approach complements the…
Phase-locked solutions of coupled oscillators are studied with asymmetric coupling strengths or inhomogeneous natural frequencies. The solutions show remarkable profiles of phase lags from the pacemaker corresponding to the ratio of upward…
Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator…
We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of…
We study numerically the oscillation death state in the phase oscillator model proposed byWinfree. We found that the phases in this state follow very simple rules, actually, besides intrinsic properties of the oscillators, such as natural…
A regime of coexistence of asynchronous and clustered dynamics is analyzed for globally coupled homogeneous and heterogeneous inhibitory networks of quadratic integrate-and-fire (QIF) neurons subject to Gaussian noise. The analysis is based…
In a recent paper, Diaz-Guilera et al. [Phys. Rev. E 57, 3820 (1998)] analyze the mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators. In essence, their analysis consists in the study of the…
In this work, we explore a new approach to synchronization of coupled oscillators. In contrast to the celebrated Kuramoto model we do not work in polar coordinates and do not consider oscillations of fixed magnitude. We propose a…
In a recent paper [Chaos 30, 073139 (2020)] we analyzed an extension of the Winfree model with nonlinear interactions. The nonlinear coupling function Q was mistakenly identified with the non-infinitesimal phase-response curve (PRC). Here,…
We study a model of coupled oscillators with bidirectional first nearest neighbours coupling with periodic boundary conditions. We show that a stable phase-locked solution is decided by the oscillators at the borders between the major…
Decentralized heading control is crucial for robotic network operations such as surveillance, exploration, and cooperative construction. However, few results consider decentralized heading control when the speed of heading adjustment is…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
Synchronization is a hallmark of collective behavior that emerges when nonlinear systems interact, spanning scales from mechanical oscillators to planetary orbits. As a universal phenomenon it underpins the study of complex systems and has…
Phase reduction is a dimensionality reduction scheme to describe the dynamics of nonlinear oscillators with a single phase variable. While it is crucial in synchronization analysis of coupled oscillators, analytical results are limited to…
Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may…
We consider discontinuous dynamics of integrate-and-fire models, which consist of pulse-coupled biological oscillators. A thoroughly constructed map is in the basis of the analysis. Synchronization of non-identical oscillators is…
The global structure of the Isochrons and the corresponding Phase Response Curves are, for the first time, investigated and numerically computed for the fundamental photonic oscillator consisted of an Optically Injected Laser. Their crucial…