Stochastic response analysis of a birhythmic oscillator under Poisson white noise excitation via path integration method
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View abstract on PubMed
Summary
This summary is machine-generated.This study analyzes the birhythmic Van der Pol oscillator under Poisson white noise. Nonlinear parameters critically affect how noise impacts the system
Area Of Science
- Nonlinear Dynamics
- Stochastic Processes
- Oscillator Systems
Background
- The Van der Pol oscillator is a classical model exhibiting complex dynamics.
- Understanding oscillator response to random disturbances is crucial in various scientific fields.
- Birhythmic systems display multiple stable states, adding complexity to their stochastic analysis.
Purpose Of The Study
- To investigate the stochastic response of a birhythmic Van der Pol oscillator subjected to Poisson white noise excitation.
- To develop and validate an improved path integration (PI) method for calculating the system's probability density.
- To analyze the influence of nonlinear parameters and Poisson white noise characteristics on both stationary and transient responses.
Main Methods
- Derivation and application of an improved path integration (PI) method.
- Calculation of the system's probability density using the PI method.
- Validation of the PI method through Monte Carlo simulations.
Main Results
- Nonlinear system parameters significantly dictate the impact of Poisson white noise on the birhythmic oscillator.
- Comparison of Poisson and Gaussian white noise effects at equivalent intensities reveals distinct mechanisms.
- Key parameters of Poisson noise were analyzed for their influence on stationary and transient dynamics.
Conclusions
- The improved PI method accurately captures the stochastic behavior of the birhythmic Van der Pol oscillator.
- Nonlinear parameters are pivotal in governing the system's response to random perturbations, including the timing of birhythmicity.
- This research offers insights into the dynamics of oscillators under discontinuous stochastic disturbances.
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