Analysis framework for stochastic predator–prey model with demographic noise

Most existing studies focus on environmental noise, with few studies focusing on pure demographic noise. We propose an analytical framework that applies stochastic differential equation tools to prove the well-posedness of solutions to such models with pure demographic noise and obtain moment and asymptotic bounds. We use this framework to prove that demographic noise does not lead to population extinction, and numerical results are consistent with it. Our proposed framework fills the gaps in research on the well-posedness and extinction impossibility of models with pure demographic noise and provides a rigorous mathematical framework for addressing a general ecology system in more sophisticated evolutionary setups.