Related papers: Stable Chimera States: A Geometric Singular Pertur…
We study the stability properties and long-term dynamical behavior of chimera states in globally coupled map lattices. In particular, we give a formula for the transverse Lyapunov exponent associated with blocks of synchronized sites. We…
We investigate "chimera" states in a ring of identical phase oscillators coupled in a time-delayed and spatially non-local fashion. We find novel "clustered chimera" states that have spatially distributed phase coherence separated by…
Chimera states, characterized by the coexistence of coherent and incoherent domains, represent a paradigm of self-organization in complex systems. In this study, we introduce a topological analysis method based on winding numbers to…
Aiming at the core problem that it is difficult for a fixed inertia coefficient to balance transient disturbance suppression and long-term stability in complex network synchronization systems, an adaptive inertia control strategy based on…
Using recent dimensionality reduction techniques in large systems of coupled phase oscillators exhibiting bistability, we analyze complex macroscopic behavior arising when the coupling between oscillators is allowed to evolve slowly as a…
Oscillatory media can exhibit the coexistence of synchronized and desynchronized regions, so-called chimera states, for uniform parameters and symmetrical coupling. In a phase-balanced chimera state, where the totals of synchronized and…
This paper presents the notion of stochastic phase-cohesiveness based on the concept of recurrent Markov chains and studies the conditions under which a discrete-time stochastic Kuramoto model is phase-cohesive. It is assumed that the…
Chimera states, which consist of coexisting domains of coherent and incoherent parts, have been observed in a variety of systems. Most of previous works on chimera states have taken into account specific form of interaction between…
Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We analyse chimera states in networks of Van der Pol oscillators with hierarchical coupling topology. We investigate…
The Kuramoto model is a canonical model for understanding phase-locking phenomenon. It is well-understood that, in the usual mean-field scaling, full phase-locking is unlikely and that it is partially phase-locked states that are important…
The Kuramoto model provides a concrete mathematical realization of emergent synchrony in a population of phase-coupled oscillators. Since Kuramoto's publication, \textit{Oscillations, Waves, and Turbulence}, researchers have worked to…
We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent…
We consider an infinite network of globally-coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when…
We study networks of non-locally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network…
Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked oscillators coexist with drifting ones. Discovered two years ago, such "chimera states" are believed to be impossible for locally or…
We report the appearance and the metamorphoses of spiral wave chimera states in coupled phase oscillators with inertia. First, when the coupling strength is small enough, the system behavior resembles classical two-dimensional (2D)…
Motivated by recent observations in neuronal systems we investigate all-to-all networks of non-identical oscillators with adaptive coupling. The adaptation models spike-timing-dependent plasticity in which the sum of the weights of all…
By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…
How higher-order interactions influence the dynamics of second order phase oscillators? We address this question using three coupled Kuramoto phase oscillators with inertia under both pairwise and higher order interactions, finding…
We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic,…