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Updated: May 9, 2026
09:10
Fabrication and Testing of Microfluidic Optomechanical Oscillators
Published on: May 29, 2014
Exploring a noisy van der Pol type oscillator with a stochastic approach.
Ruoshi Yuan1, Xinan Wang, Yian Ma
1Key Laboratory of Systems Biomedicine, Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai, 200240, China.
Summary
A novel stochastic interpretation simplifies the analysis of deterministic dynamics with multiplicative noise. This approach reveals that steady-state distributions are Boltzmann-Gibbs type, with attractors corresponding to extrema of the distribution function.
Area of Science:
- Nonlinear dynamics
- Statistical physics
- Stochastic processes
Background:
- Conventional interpretations (Ito, Stratonovich) of multiplicative noise complicate the analysis of deterministic systems.
- Zero-mean multiplicative noise can alter system dynamics, including attractor shifts and topological changes.
Purpose of the Study:
- To introduce a new stochastic interpretation for analyzing systems with multiplicative noise.
- To simplify the understanding of how noise affects deterministic dynamics.
- To analyze nonequilibrium processes, specifically noisy limit cycle dynamics.
Main Methods:
- Employing a new stochastic interpretation of multiplicative noise.
- Analyzing the resulting steady-state distribution.
- Investigating noisy limit cycle dynamics, including van der Pol oscillators.
Main Results:
- The new interpretation yields a Boltzmann-Gibbs type steady-state distribution.
- A potential function acts as a Lyapunov function for the deterministic dynamics.
- Attractors correspond to local extrema of the distribution function, with equal probability on the attractor.
Conclusions:
- This interpretation offers a simplified approach to systems with multiplicative noise.
- It provides new insights into understanding processes lacking detailed balance.
- The findings are experimentally verifiable and applicable to various limit cycle dynamics.
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