Persistence and ergodicity of a stochastic single species model with Allee effect under regime switching

• Published in: Communications in nonlinear science & numerical simulation Vol. 59; pp. 359 - 374
• Main Authors: Yu, Xingwang, Yuan, Sanling, Zhang, Tonghua
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.06.2018; Elsevier Science Ltd
• Subjects: Allee effect; Computer simulation; Ergodic processes; Ergodicity; Extinction; Liapunov functions; Mathematical models; Numerical analysis; Regime switching; Simulation; Stochastic models; Stochastic single species model; Studies; Survival analysis; Switching; Survival analysis; Stochastic single species model; 92B05; Regime switching; Allee effect; Ergodicity; 60J28; 37H10
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2017.11.028

Allee effect can interact with environment stochasticity and is active when population numbers are small. Our goal of this paper is to investigate such effect on population dynamics. More precisely, we develop and investigate a stochastic single species model with Allee effect under regime switching. We first prove the existence of global positive solution of the model. Then, we perform the survival analysis to seek sufficient conditions for the extinction, non-persistence in mean, persistence in mean and stochastic permanence. By constructing a suitable Lyapunov function, we show that the model is positive recurrent and ergodic. Our results indicate that the regime switching can suppress the extinction of the species. Finally, numerical simulations are carried out to illustrate the obtained theoretical results, where a real-life example is also discussed showing the inclusion of Allee effect in the model provides a better match to the data.