Noise-induced standing waves in oscillatory systems with time-delayed feedback

TL;DR

This paper demonstrates that additive Gaussian white noise can induce standing waves in oscillatory reaction-diffusion systems with time-delay feedback, especially near phase boundaries, by combining analytical and simulation approaches.

Contribution

It reveals how noise can promote standing waves in systems where deterministic dynamics stabilize uniform oscillations, highlighting the interplay between noise and reaction-diffusion feedback.

Findings

Noise can induce standing waves near deterministic phase boundaries.

Small noise can trigger standing waves even when deterministic modes are stable.

Larger noise levels can induce standing waves away from phase boundaries.

Abstract

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 spatio-temporal 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 spatio-temporal 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.