title: Exploring a noisy van der Pol type oscillator with a stochastic approach.
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.
authors.affiliation: Key Laboratory of Systems Biomedicine, Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai, 200240, China.
authors.forename: Ruoshi
authors.initials: R
authors.lastname: Yuan
authors.forename: Xinan
authors.initials: X
authors.lastname: Wang
authors.forename: Yian
authors.initials: Y
authors.lastname: Ma
authors.forename: Bo
authors.initials: B
authors.lastname: Yuan
authors.forename: Ping
authors.initials: P
authors.lastname: Ao
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D015233:Models, Statistical; D009991:Oscillometry / Q000379:methods*; D059629:Signal-To-Noise Ratio; D013269:Stochastic Processes