Related papers: Synchronization dynamics of phase oscillators on p…
The collective behavior of the ensembles of coupled nonlinear oscillator is one of the most interesting and important problems in modern nonlinear dynamics. In this paper, we study rotational dynamics, in particular space-time structures,…
A model for synchronization of globally coupled phase oscillators including ``inertial'' effects is analyzed. In such a model, both oscillator frequencies and phases evolve in time. Stationary solutions include incoherent (unsynchronized)…
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…
We propose a mathematical framework for designing robust networks of coupled phase-oscillators by leveraging a vulnerability measure proposed by Tyloo et. al that quantifies how much a small perturbation to a phase-oscillator's natural…
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…
We characterize the synchronization of an array of coupled chaotic elements as a phase transition where order parameters related to the joint probability at two sites obey power laws versus the mutual coupling strength; the phase transition…
Two types of phase synchronization (accordingly, two scenarios of breaking phase synchronization) between coupled stochastic oscillators are shown to exist depending on the discrepancy between the control parameters of interacting…
We study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher-order modes dominate the coupling between oscillators. For the first time, we develop a complete analytic description of the…
We investigate the entrainment of a neuron model exhibiting a chaotic spiking-bursting behavior in response to a weak periodic force. This model exhibits two types of oscillations with different characteristic time scales, namely, long and…
We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider extensions to networks with mixed…
We study fully synchronized (coherent) states in complex networks of chaotic oscillators, reviewing the analytical approach of determining the stability conditions for synchronizability and comparing them with numerical criteria. As an…
We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective…
We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to a number of states unsupported by…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…
We study the dynamics of network-coupled phase oscillators in the presence of coupling frustration. It was recently demonstrated that in heterogeneous network topologies, the presence of coupling frustration causes perfect phase…
Coupled oscillator networks show a complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these…
Many oscillator networks are multistable, meaning that different synchronization states are realized depending on the initial conditions. In this paper, we numerically analyze a ring network of phase oscillators, in which synchronous states…
The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications…
The mechanism of phase synchronization between uncoupled limit-cycle oscillators induced by common external impulsive forcing is analyzed. By reducing the dynamics of the oscillator to a random phase map, it is shown that phase…
Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the strength of coupling often leads to qualitative changes in the complex dynamics of the mutually coupled…