2016/05/23 by Michael Stich, Amit K. Chattopadhyay, Amit K Chattopadhyay · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Acoustics #Boundary (topology) #Classical mechanics #Computer science #Control theory (sociology) #Diffusion #Forcing (mathematics) #Instability #Mathematical analysis #Mathematics #Mechanics #Noise (video) #Nonlinear Dynamics and Pattern Formation #Phase (matter) #Physics #Quantum mechanics #Reaction–diffusion system #Spectroscopy and Quantum Chemical Studies #Standing wave #Statistical physics #White noise #cond-mat.soft #cond-mat.stat-mech #nlin.PS #physics.bio-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.93.052221
published in Physical review. E 93(5), 052221 (American Physical Society) · 8 two-columned pages, 5 figures; Published in PRE; URL: http://link.aps.org/doi/10.1103/PhysRevE.93.05222
openalex publication_date 2016/05/23 · arxiv created 2016/05/27 · arxiv updated 2016/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can induce the appearance of standing waves. Combining analytical solutions of the model with spatiotemporal simulations, we find that noise can promote standing waves in regimes where the deterministic uniform oscillatory modes are stabilized. As the deterministic phase boundary is approached, the spatiotemporal correlations become stronger, such that even small noise can induce standing waves in this parameter regime. With larger noise strengths, standing waves could be induced at finite distances from the (deterministic) phase boundary. The overall dynamics is defined through the interplay of noisy forcing with the inherent reaction-diffusion dynamics.