Abstract
We study a stochastic logistic model with diffusion between two patches in this paper. Using the definition of stationary distribution, we discuss the effect of dispersal in detail. If the species are able to have nontrivial stationary distributions when the patches are isolated, then they continue to do so for small diffusion rates. In addition, we use some examples and numerical experiments to reflect that diffusions are capable of both stabilizing and destabilizing a given ecosystem.
Highlights
Dispersal is a ubiquitous phenomenon in the natural world
Takeuchi [9] has proved that this single species diffusion model has a positive and globally stable equilibrium point E∗(x1∗, x2∗) for any diffusion rate; the results obtained in his paper show that no diffusion rate; can change the global stability of the deterministic model
The main objective of this paper is to study the effects of dispersal on stationary distribution for a stochastic logistic diffusion system
Summary
Dispersal is a ubiquitous phenomenon in the natural world This phenomenon plays a very important role in understanding the ecological and evolutionary dynamics of populations. The others dealt with competition or predator-prey interactions in patchy environments (see [10,11,12,13,14,15,16] and references cited therein) These models centered round local and global stability of equilibrium points, persistence, and extinction of populations. We will investigate the effects of dispersal by the concept of stationary distribution (some analogue which plays the role of the deterministic equilibrium point and reflects the stability to some extent). Diffusions are capable of both stabilizing and destabilizing a given ecosystem
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
