Czechoslovak Mathematical Journal, Vol. 67, No. 4, pp. 867-890, 2017
Population dynamical behavior of a single-species nonlinear diffusion system with random perturbation
Li Zu, Daqing Jiang, Donal O'Regan
Received June 28, 2015. First published October 24, 2017.
Abstract: We consider a single-species stochastic logistic model with the population's nonlinear diffusion between two patches. We prove the system is stochastically permanent and persistent in mean, and then we obtain sufficient conditions for stationary distribution and extinction. Finally, we illustrate our conclusions through numerical simulation.
Keywords: stochastic permanence; persistent in mean; extinction; stationary distribution
Affiliations: Li Zu, College of Mathematics and Statistics, Hainan Normal University, Longkun South Road, Hainan 571158, Haikou, Hainan, China, e-mail: firstname.lastname@example.org; Daqing Jiang (corresponding author), School of Science, China University of Petroleum, 66 Changjiang West Road, Qingdao 266580, Huangdao, Shandong, China, and Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, King Abdulaziz University, Umm Al Muminin, Al-Sharafeyah, Jeddah 23218, Saudi Arabia, e-mail: email@example.com; Donal O'Regan, School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, University Road, Galway H91 TK33, Ireland, e-mail: firstname.lastname@example.org