Related papers: Correspondence between Phase Oscillator Network an…
Kuramoto oscillators have been proposed earlier as a model for interacting systems that exhibit synchronisation. In this article we study the difference between networks with symmetric and asymmetric distribution of natural frequencies. We…
We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…
We introduce a solvable spherical model of coupled oscillators with fully random interactions and distributed natural frequencies. Using the dynamical mean-field theory, we derive self-consistent equations for the steady-state response and…
We investigate synchronization effects in quantum self-sustained oscillators theoretically using the micromaser as a model system. We use the probability distribution for the relative phase as a tool for quantifying the emergence of…
We study the effects of a probabilistic refractory period in the collective behavior of coupled discrete-time excitable cells (SIRS-like cellular automata). Using mean-field analysis and simulations, we show that a synchronized phase with…
Oscillator networks found in social and biological systems are characterized by the presence of wide ranges of coupling strengths and complex organization. Yet robustness and synchronization of oscillations are found to emerge on…
We present a theory to describe the dynamics of the Sherrington- Kirkpatrick spin-glass with (sequential) Glauber dynamics in terms of deterministic flow equations for macroscopic parameters. Two transparent assumptions allow us to close…
We study the phase-synchronization properties of systolic and diastolic arterial pressure in healthy subjects. We find that delays in the oscillatory components of the time series depend on the frequency bands that are considered, in…
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…
This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and…
In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system…
Oscillator networks with an asymmetric bipolar distribution of natural frequencies are useful representations of power grids. We propose a mean-field model that captures the onset, form and linear stability of frequency synchronization in…
Synchronization of neurons forming a network with a hierarchical structure is essential for the brain to be able to function optimally. In this paper we study synchronization of phase oscillators on the most basic example of such a network,…
In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging generalization of the SK model, such settings may arise…
The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator…
In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others…
Many systems of physical and biological interest are characterized by assemblies of phase oscillators whose interaction is mediated by a diffusing chemical. The coupling effect results from the fact that the local concentration of the…
We develop a general theoretical framework of semiclassical phase reduction for analyzing synchronization of quantum limit-cycle oscillators. The dynamics of quantum dissipative systems exhibiting limit-cycle oscillations are reduced to a…
We compare the quantum and classical properties of the (Quantum) Isoperiodic Stable Structures -- (Q)ISSs -- which organize the parameter space of a paradigmatic dissipative ratchet model, i.e. the dissipative modified kicked rotator. We…
Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay…