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Noise-induced stabilization of collective dynamics
Pau Clusella1,2, Antonio Politi1
1Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.
Physical Review. E
|July 16, 2017
Summary
A small amount of white noise can unexpectedly stabilize unstable collective behavior in coupled oscillators. This stochastic force also broadens clusters, revealing new insights into system dynamics.
Area of Science:
- Physics
- Nonlinear Dynamics
- Statistical Mechanics
Background:
- Globally coupled oscillators are fundamental in various scientific fields.
- Understanding the influence of noise on system stability is crucial.
- Deterministic forces can induce clustering in oscillator ensembles.
Purpose of the Study:
- To investigate the counterintuitive effects of additive stochastic force on coupled oscillators.
- To demonstrate noise-induced stabilization of unstable collective periodic regimes.
- To identify and analyze noise-induced bifurcations.
Main Methods:
- Microscopic simulations of globally coupled oscillators.
- Perturbative solution of the nonlinear Fokker-Planck equation.
- Macroscopic analysis to determine stability eigenvalues.
Main Results:
- White noise broadens clusters induced by deterministic forces.
- A small amount of white noise stabilizes a linearly unstable collective periodic regime (self-consistent partial synchrony).
- Two noise-induced bifurcations were identified.
Conclusions:
- Stochastic forces can have stabilizing effects in nonlinear systems.
- The findings suggest a broader applicability of noise-induced stabilization in complex systems.
- The phenomenon's generality is discussed.
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