The most probable transition pathway of a predator–prey system under noise

Abstract

Stochastic population dynamics plays a crucial role in biological systems. The number and distribution of biological populations often affect the stability of ecosystems, and even lead to the transition of ecosystems from one steady-state to another. The transition between different states of a population has a significant impact on both population dynamics and biological evolution. In this paper, we examined a stochastic population model and used Onsager–Machlup action functional and neural shooting method to obtain the most probable transition pathway between different states. Moreover, we analyzed the influence of noise intensity, maximum harvest rate [Formula: see text] and time [Formula: see text] on most probable transition pathway in two different parameter scenarios. Our research may provide a better understanding of evolutionary process such as genetic variation in populations and the evolution of species adaptation, meanwhile, may provide a theoretical guidance for species conservation and management in real world.