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Noise-induced standing waves in oscillatory systems with time-delayed feedback.
Michael Stich1, Amit K Chattopadhyay1
1Non-linearity and Complexity Research Group, Systems Analytics Research Institute, School of Engineering and Applied Science, Aston University, Aston Triangle, Birmingham, B4 7ET, United Kingdom.
Physical Review. E
|June 15, 2016
Summary
Noise can induce standing waves in oscillatory reaction-diffusion systems. Even small amounts of Gaussian white noise can stabilize uniform oscillations, promoting standing wave formation near phase boundaries.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Chemical kinetics
Background:
- Oscillatory reaction-diffusion systems exhibit complex spatiotemporal patterns.
- Time-delay feedback can destabilize uniform oscillations, leading to standing wave formation.
- The role of noise in pattern formation within these systems is not fully understood.
Purpose of the Study:
- To investigate the influence of additive Gaussian white noise on standing wave formation in oscillatory reaction-diffusion systems.
- To determine how noise affects the stability of uniform oscillatory modes.
- To explore the conditions under which noise can induce standing waves.
Main Methods:
- Analytical solutions of the reaction-diffusion model.
- Spatiotemporal simulations of the system dynamics.
- Analysis of the interplay between noisy forcing and reaction-diffusion dynamics.
Main Results:
- Gaussian white noise can induce standing waves in parameter regimes where deterministic uniform oscillatory modes are stable.
- Noise promotes standing wave formation as the deterministic phase boundary is approached due to strengthened spatiotemporal correlations.
- Larger noise strengths can induce standing waves even at finite distances from the deterministic phase boundary.
Conclusions:
- Additive noise plays a crucial role in pattern selection within oscillatory reaction-diffusion systems.
- Noise can act as a mechanism to generate standing waves, complementing deterministic instabilities.
- The interplay between noise and inherent system dynamics governs the emergence of complex spatiotemporal patterns.
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