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Updated: May 26, 2026
12:03
A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
Published on: May 25, 2019
Noise-controlled dynamics through the averaging principle for stochastic slow-fast systems.
1Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 13, Villetaneuse, France. wainrib@math.univ-paris13.fr
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
Noise can surprisingly control dynamics in nonlinear systems. This study reveals how specific noise levels and time-scale separation can induce or suppress oscillations in excitable systems, offering insights into biological noise control.
Area of Science:
- Nonlinear dynamics
- Stochastic systems
- Computational neuroscience
Background:
- Noise perturbations can induce limit cycles in excitable systems via self-induced stochastic resonance (SISR).
- Understanding noise effects in slow-fast nonlinear systems is crucial for biological modeling.
Purpose of the Study:
- To analyze the impact of order 1 noise on coupled FitzHugh-Nagumo systems.
- To investigate noise-induced behaviors and the role of stochastic averaging.
Main Methods:
- Utilized the stochastic averaging principle.
- Modeled a system of two coupled FitzHugh-Nagumo equations.
- Analyzed system behavior across varying noise intensities.
Main Results:
- Observed noise-free resting state fluctuations.
- Confirmed oscillations due to SISR at small noise levels.
- Identified a return to resting state fluctuations at intermediate noise.
- Detected new oscillations at larger noise intensities, explained by stochastic averaging.
Conclusions:
- Time-scale separation in biological systems may function as a noise averager.
- This mechanism enables noise-controlled dynamical behavior through averaging.
- Findings offer a novel perspective on noise regulation in biological systems.
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