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

Abstract

The existing research studies on the basin stability of stochastic systems typically focus on smooth systems, or the attraction basins are pre-defined as easily solvable regular basins. In this work, we introduce a new framework to discover the basin stability from state time series in the non-smooth stochastic competition system under threshold control. Specifically, we approximate the drift and diffusion with threshold control parameters by an extended Kramers-Moyal expansion with initial state partitioning. Then, we calculate the first transition probability of irregular attraction basins by applying a difference scheme and smooth approximation methods for the system. Numerical simulations of the original system validate the accuracy of the identified drift and diffusion terms, as well as the smooth approximation. Our findings reveal that threshold control modifies the influence of environmental noise on the system basin stability.