Discovering stochastic basin stability from data in a Filippov competition system with threshold control

Area of Science:

• Stochastic Systems Analysis
• Non-smooth Dynamics
• Computational Physics

Background:

• Existing research on basin stability often simplifies systems to smooth models or pre-defined basins.
• Analyzing non-smooth stochastic systems, especially with threshold control, presents significant challenges.
• Understanding basin stability is crucial for predicting system behavior under uncertainty.

Purpose of the Study:

• To develop a novel framework for discovering basin stability in non-smooth stochastic competition systems with threshold control.
• To analyze the impact of threshold control on system dynamics and environmental noise.
• To provide a method for calculating the first transition probability of irregular attraction basins.

Main Methods:

• Utilized an extended Kramers-Moyal expansion with initial state partitioning to approximate drift and diffusion terms.
• Applied difference schemes and smooth approximation methods to calculate the first transition probability for irregular basins.
• Employed numerical simulations to validate the accuracy of the approximated terms and methods.

Main Results:

• Successfully approximated drift and diffusion terms in a non-smooth stochastic system under threshold control.
• Validated the accuracy of the approximation methods through numerical simulations.
• Demonstrated that threshold control parameters influence the system's basin stability in response to environmental noise.

Conclusions:

• The developed framework effectively identifies basin stability in complex, non-smooth stochastic systems.
• Threshold control plays a critical role in modulating the effects of environmental noise on system dynamics.
• This research offers new insights into the behavior of stochastic systems with practical control mechanisms.