Exact Mapping Noisy van der Pol Type Oscillator onto Quasi-symplectic Dynamics

TL;DR

This paper establishes an exact mapping of noisy van der Pol oscillators onto quasi-symplectic dynamics, revealing a dual role potential and steady state distribution, offering new insights into non-equilibrium processes.

Contribution

It introduces a novel exact mapping for noisy limit cycle systems onto quasi-symplectic dynamics, including a dual role potential and a new stochastic interpretation.

Findings

Steady state distribution follows Boltzmann-Gibbs form for any noise level.

Provides a new framework for understanding non-equilibrium systems without detailed balance.

Verifiable through experimental validation.

Abstract

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.