Related papers: Contraction of monotone phase-coupled oscillators
Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the…
We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…
We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
We study the synchronization transition of Kuramoto oscillators in scale-free networks that are characterized by tunable local properties. Specifically, we perform a detailed finite size scaling analysis and inspect how the critical…
In this brief tutorial review, I show how phase coherent properties of disordered conductors can be described in a simple and unified way. These properties include transport properties like weak-localization correction and universal…
We propose the definition of the geometric measure of entanglement for continuous variable states. On the basis of this definition we examine entanglement of the graph states obtained as a result of action of a unitary operator on the…
In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \cite{Lohmiller98} to random differential equations. We propose new definitions of…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
Monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties. It is known that under the property of quasimonotonicity…
We study the versatile performance of networks of coupled circuits. Each of these circuits is composed of a positive and a negative feedback loop in a motif that is frequently found in genetic and neural networks. When two of these circuits…
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…
The particular properties of synchronization are discussed for coupled auto-oscillating systems, which are characterized by non-quadratic law of potential dependence on the coordinate. In particular, structure of the parameter plane…
This paper introduce the notion of output contraction that expands the contraction notion to the time-varying nonlinear systems with output. It pertains to the systems' property that any pair of outputs from the system converge to each…
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…
Topological ordered phases are related to changes in the properties of their quasi-particle excitations (anyons). We study these relations in the framework of projected entanglement pair states (\textsf{PEPS}) and show how condensing and…
A generalized Kuramoto model of coupled phase oscillators with slowly varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs of oscillators in such a way that the coupling…
We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.
Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we…
We consider an ensemble of globally coupled phase oscillators whose interaction is transmitted at finite speed. This introduces time delays, which make the spatial coordinates relevant in spite of the infinite range of the interaction. We…