Dependence of metrics and noise intensity on escape dynamics: mean first exit time and escape probability

Abstract This paper focuses on analyzing two deterministic quantities of the dynamics of stochastic systems, mean first exit time and escape probability. Through a detailed exploration of the escape phenomenon, we have successfully fitted the complex dynamics of the mean first exit time as a function of interval length (area size) and noise intensity, respectively. We have found that the mean first exit time tends to increase monotonically with the interval length (area size). Meanwhile, we also accurately captured the dynamical behavior of the minimum escape probability under various parameter cases. The relationship between them displays a range of patterns when we observed different intervals. Our research highlights the importance of noise effects when considering escape processes, especially in the context of interaction of interval length (area size) and noise intensity. A concrete error analysis is conducted to ensure the accuracy and generalization ability of the model’s predictions.