Arrays of stochastic oscillators: Nonlocal coupling, clustering, and wave formation

Abstract

We consider an array of units each of which can be in one of three states. Unidirectional transitions between these states are governed by Markovian rate processes.The interactions between units occur through a dependence of the transition rates of a unit on the states of the units with which it interacts. This coupling is nonlocal, that is, it is neither an all-to-all interaction (referred as global coupling), nor is it a nearest neighbor interaction (referred to as local coupling).The coupling is chosen so as to disfavor the crowding of interacting units in the same state. As a result, there is no global synchronization. Instead, the resultant spatiotemporal configuration is one of clusters that move at a constant speed and that can be interpreted as \emph{traveling waves}. We develop a mean field theory to describe the cluster formation and analyze this model analytically. The predictions of the model are compared favorably with the results obtained by direct numerical simulations.

References in corpus (24)

• The World of the Complex Ginzburg-Landau Equation
• Chimera States for Coupled Oscillators
• Solvable model for chimera states of coupled oscillators
• Collapse arrest and soliton stabilization in nonlocal nonlinear media
• Modulational instability in nonlocal nonlinear Kerr media
• Non-local Interaction Effects on Pattern Formation in Population Dynamics
• Stochastic Turing patterns in the Brusselator model
• Robust ecological pattern formation induced by demographic noise
• Thermally Induced Fluctuations Below the Onset of Rayleigh-Bénard Convection
• Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates
• Multipole vector solitons in nonlocal nonlinear media
• The universality of synchrony: critical behavior in a discrete model of stochastic phase coupled oscillators
• Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures
• Fluctuations impact on a pattern-forming model of population dynamics with non-local interactions
• Critical behavior and synchronization of discrete stochastic phase coupled oscillators
• Continuous and discontinuous phase transitions and partial synchronization in stochastic three-state oscillators
• Coupled three-state oscillators
• Effects of Disorder on Synchronization of Discrete Phase-Coupled Oscillators
• Spatial patterns in mesic savannas: the local facilitation limit and the role of demographic stochasticity
• Nonlocality-induced front interaction enhancement
• An infinite-period phase transition versus nucleation in a stochastic model of collective oscillations
• Competitive Brownian and Levy walkers
• Synchronization of globally coupled two-state stochastic oscillators with a state dependent refractory period
• Collective behavior of coupled nonuniform stochastic oscillators

Cited by in corpus (7)

• Collective power: Minimal model for thermodynamics of nonequilibrium phase transitions
• Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes
• A continuous-time persistent random walk model for flocking
• Stochastic Kuramoto oscillators with discrete phase states
• Synchronization of coupled noisy oscillators: Coarse-graining from continuous to discrete phases
• Synchronization and phase redistribution in self-replicating populations of coupled oscillators and excitable elements
• Dissipation enables robust extensive scaling of multipartite correlations