Phase reduction of stochastic limit cycle oscillators

Area of Science:

• Nonlinear Dynamics
• Stochastic Processes
• Oscillator Systems

Background:

• The conventional phase equation is widely used to approximate oscillator behavior under noise.
• However, its validity, especially for weak noise levels, has been questioned.
• Accurate modeling of noisy oscillators is crucial in various scientific and engineering fields.

Purpose of the Study:

• To present a novel phase reduction method for oscillators subjected to weak white Gaussian noise.
• To validate the accuracy of this new method compared to the conventional approach.
• To investigate the impact of noise on oscillator frequency and entrainment phenomena.

Main Methods:

• Development of a new phase reduction technique applicable to weak white Gaussian noise.
• Numerical simulations to compare the dynamics predicted by the new method and the original oscillator.
• Analysis of frequency shifts and entrainment behavior under varying noise conditions.

Main Results:

• The proposed phase reduction method accurately approximates the dynamics of oscillators with weak white Gaussian noise.
• Numerical evidence supports the effectiveness of the new method.
• Noise is shown to induce a general shift in the oscillator's frequency.

Conclusions:

• The conventional phase equation is an insufficient approximation for noisy oscillators, even at low noise levels.
• The developed phase reduction method offers a more accurate description of oscillator dynamics under weak noise.
• Noise-induced frequency shifts significantly impact oscillator entrainment.