Effects of disorder on synchronization of discrete phase-coupled oscillators.

  title={Effects of disorder on synchronization of discrete phase-coupled oscillators.},
  author={Kevin Wood and Christian Van den Broeck and Ryoichi Kawai and Katja Lindenberg},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={75 4 Pt 1},
We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of globally connected arrays of N types of oscillators (N=2,3,4) by exploring the linear stability of the nonsynchronous fixed point. We also provide results for globally coupled arrays where the transition rate of each unit is drawn from a uniform distribution of… 

Globally coupled stochastic two-state oscillators: synchronization of infinite and finite arrays

We consider arrays of the simplest two-state (on–off) stochastic units. The units are Markovian, that is, the transitions between the two states occur at a given rate. We construct arrays of N

Phase transitions and entropies for synchronizing oscillators.

It is quantitatively account for how the synchronized pulse is a low-entropy structure that facilitates the production of more entropy by the system as a whole and how a phase transition occurs when the coupling parameter is varied.

Synchronization of discrete oscillators on ring lattices and small-world networks

A lattice of three-state stochastic phase-coupled oscillators exhibits a phase transition at a critical value of the coupling parameter a, leading to stable global oscillations. On a complete graph,

Collective oscillations of excitable elements: order parameters, bistability and the role of stochasticity

It is shown that a synchronized phase with stable collective oscillations exists even with non-deterministic refractory periods, and the mean-field prediction agrees quantitatively with simulations of complete graphs and, for random graphs, qualitatively predicts the overall structure of the phase diagram.

An infinite-period phase transition versus nucleation in a stochastic model of collective oscillations

A lattice model of three-state stochastic phase-coupled oscillators has been shown by Wood et al (2006 Phys. Rev. Lett. 96 145701) to exhibit a phase transition at a critical value of the coupling

Synchronization and fluctuations: Coupling a finite number of stochastic units.

The finite-N problem is addressed by deducing a Fokker-Planck equation that describes the system and the steady-state solution is computed, which is used to analyze the synchronic properties of the system in the framework of the different order parameters that have been proposed in the literature to study nonequilibrium transitions.

Synchronization, stickiness effects and intermittent oscillations in coupled nonlinear stochastic networks

Long distance reactive and diffusive coupling is introduced in a spatially extended nonlinear stochastic network of interacting particles. The network serves as a substrate for Lotka-Volterra

Species mobility induces synchronization in chaotic population dynamics.

A prototype population dynamics model with cyclic domination of four species and empty sites is proposed for studying transition to synchronization, showing quasiperiodicity and chaos depending on the parameter values.



Nonlinear Dynamics And Chaos

The logistic map, a canonical one-dimensional system exhibiting surprisingly complex and aperiodic behavior, is modeled as a function of its chaotic parameter, and the progression through period-doubling bifurcations to the onset of chaos is considered.

Chemical oscillations

A chemical reaction is usually thought of as coming together of reactant molecules to form products. The concentrations of initial components (reactants) decrease, and concentrations of products

Chemical Oscillations, Waves, and Turbulence

Synchronization - A Universal Concept in Nonlinear Sciences

This work discusseschronization of complex dynamics by external forces, which involves synchronization of self-sustained oscillators and their phase, and its applications in oscillatory media and complex systems.

Physica A 325

  • 176
  • 2003

and M

  • Ignaccolo, arXiv:cond-mat/0611035
  • 2006

͑1987͒; H. Daido

  • ͑1987͒; H. Daido
  • 1005

J. Theor. Biol

  • J. Theor. Biol