System Of Kuramoto Oscillators Research Articles

Synchronization in a system of Kuramoto oscillators with distributed Gaussian noise.

We consider a system of globally coupled phase-only oscillators with distributed intrinsic frequencies and evolving in the presence of distributed Gaussian white noise, namely, a Gaussian white noise whose strength for every oscillator is a specified function of its intrinsic frequency. In the absence of noise, the model reduces to the celebrated Kuramoto model of spontaneous synchronization. For two specific forms of the mentioned functional dependence and for a symmetric and unimodal distribution of the intrinsic frequencies, we unveil the rich long-time behavior that the system exhibits, which stands in stark contrast to the case in which the noise strength is the same for all the oscillators, namely, in the studied dynamics, the system may exist in either a synchronized, or an incoherent, or a time-periodic state; interestingly, all these states also appear as long-time solutions of the Kuramoto dynamics for the case of bimodal frequency distributions, but in the absence of any noise in the dynamics.

Bumps, chimera states, and Turing patterns in systems of coupled active rotators

Self-organized coherence-incoherence patterns, called chimera states, have first been reported in systems of Kuramoto oscillators. For coupled excitable units, similar patterns where coherent units are at rest are called bump states. Here, we study bumps in an array of active rotators coupled by nonlocal attraction and global repulsion. We demonstrate how they can emerge in a supercritical scenario from completely coherent Turing patterns: a single incoherent unit appears in a homoclinic bifurcation, undergoing subsequent transitions to quasiperiodic and chaotic behavior, which eventually transforms into extensive chaos with many incoherent units. We present different types of transitions and explain the formation of coherence-incoherence patterns according to the classical paradigm of short-range activation and long-range inhibition.

Inference of the High-Level Interaction Topology between the Metabolic and Cell-Cycle Oscillators from Single-Cell Dynamics.

Recent evidence suggests that the eukaryotic metabolism is an autonomous oscillator. Together with oscillating elements of the cyclin/CDK machinery, this oscillator might form a coupled oscillator system, from which cell-cycle control emerges. The topology of interactions between the metabolic oscillator and the elements of the cyclin/CDK machinery, however, remains unknown. Using single-cell metabolic and cell-cycle dynamics in yeast, and solving an inverse problem with a system of Kuramotooscillators, we inferred how the metabolic oscillator interacts with the cyclin/CDK machinery. The identified and experimentally validated interaction topology shows that the early and late cell cycle are independently driven by metabolism. While in this topology, the S phase is coordinated by START. We obtained no support for a strong interaction between early and late cell cycle. The identified high-level interaction topology will guide future efforts to discover the molecular links between metabolism and the cell cycle.

Interplay of inertia and heterogeneous dynamics in an ensemble of Kuramoto oscillators

We study the dynamic interplay between inertia and heterogeneous dynamics in an ensemble of Kuramoto oscillators. When external fields and internal forces are exerted on a system of Kuramoto oscillators, each oscillator has its own distinct dynamics, so that there is no notion of collective dynamics in the ensemble, and complete synchronization is not observed in such systems. In this paper, we study a relaxed version of synchronization, namely the “practical synchronization”, of Kuramoto oscillators, emerging from the dynamic interplay between inertia and heterogeneous decoupled dynamics. We will show that for some class of initial configurations and parameters, the fluctuation of phases and frequencies around the average values will be proportional to the inverse of the coupling strength. We provide several numerical examples, and compare these with our analytical results.