Related Experiment Video
Updated: May 9, 2026

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.
Abstract:
Based on conventional Ito or Stratonovich interpretation, zero-mean multiplicative noise can induce shifts of attractors or even changes of topology to a deterministic dynamics. Such phenomena usually introduce additional complications in analysis of these systems. We employ in this paper a new stochastic interpretation leading to a straightforward consequence: The steady state distribution is Boltzmann-Gibbs type with a potential function severing as a Lyapunov function for the deterministic dynamics. It implies that an attractor corresponds to the local extremum of the distribution function and the probability is equally distributed right on an attractor. We consider a prototype of nonequilibrium processes, noisy limit cycle dynamics. Exact results are obtained for a class of limit cycles, including a van der Pol type oscillator. These results provide a new angle for understanding processes without detailed balance and can be verified by experiments.
Related Concept Videos
Oscillations In An LC Circuit
Damped Oscillations
Although friction and other non-conservative...
RLC Circuit as a Damped Oscillator
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Forced Oscillations
Design Example: Underdamped Parallel RLC Circuit
Starting with a fixed...
Oscillations about an Equilibrium Position

