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

Michael Stich*, Amit K Chattopadhyay

*Corresponding author for this work

Research output: Contribution to journalArticle

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.
Original languageEnglish
Article number052221
Number of pages9
JournalPhysical Review E
Volume93
Issue number5
DOIs
Publication statusPublished - 23 May 2016

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Delayed Feedback
Standing Wave
standing waves
Temporal Correlation
Gaussian White Noise
Reaction-diffusion
white noise
Reaction-diffusion System
Forcing
Time Delay
Analytical Solution
time lag
Oscillation
oscillations
Simulation
simulation

Cite this

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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.",
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Noise-induced standing waves in oscillatory systems with time-delayed feedback. / Stich, Michael; Chattopadhyay, Amit K.

In: Physical Review E, Vol. 93, No. 5, 052221, 23.05.2016.

Research output: Contribution to journalArticle

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