Exact Mapping Noisy van der Pol Type Oscillator onto Quasi-symplectic   Dynamics
  We find exact mappings for a class of limit cycle systems with noise onto quasi-symplectic dynamics, including a van der Pol type oscillator. A dual role potential function is obtained as a component of the quasi-symplectic dynamics. Based on a stochastic interpretation different from the traditional Ito's and Stratonovich's, we show the corresponding steady state distribution is the familiar Boltzmann-Gibbs type for arbitrary noise strength. The result provides a new angle for understanding processes without detailed balance and can be verified by experiments. 
Ruoshi Yuan, Xinan Wang, Yian Ma, Bo Yuan, Ping Ao
cond-mat.stat-mech math-ph math.MP physics.data-an