scholarly journals Global dynamics of a Lotka-Volterra competition-diffusion-advection system for small diffusion rates in heterogenous environment

2021 ◽  
Vol 18 (1) ◽  
pp. 564-582
Author(s):  
Jinyu Wei ◽  
◽  
Bin Liu ◽  
Keyword(s):  
Global Dynamics ◽  
Small Diffusion ◽  
Diffusion Rates ◽  
Competition Diffusion

Global Dynamics of a Lotka–Volterra Competition Diffusion System with Nonlocal Effects

2020 ◽  
Vol 30 (05) ◽  
pp. 2050066 ◽  
Author(s):  
Bang-Sheng Han ◽  
Yinghui Yang ◽  
Wei-Jian Bo ◽  
Huiling Tang
Keyword(s):  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Diffusion System ◽  
Upper And Lower Bounds ◽  
Global Dynamics ◽  
Nonlocal Effects ◽  
Monotone Iteration ◽  
Existence And Nonexistence ◽  
Uniqueness Of The Solution ◽  
Competition Diffusion

This paper is concerned with the global dynamics of a Lotka–Volterra competition diffusion system having nonlocal intraspecies terms. Based on the reconstructed comparison principle and monotone iteration, the existence and uniqueness of the solution for the corresponding Cauchy problem are established. In addition, the spreading speed of the system with compactly supported initial data is considered, which admits uniform upper and lower bounds. Finally, some sufficient conditions for guaranteeing the existence and nonexistence of Turing bifurcation are given, which depend on the intensity of nonlocality. Comparing with the classical Lotka–Volterra competition diffusion system, our results indicate that a nonconstant periodic solution may exist if the nonlocality is strong enough, which are also illustrated numerically.

scholarly journals Effects of Dispersal for a Logistic Growth Population in Random Environments

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaoling Zou ◽  
Dejun Fan ◽  
Ke Wang
Keyword(s):  
Stationary Distribution ◽  
Logistic Model ◽  
Numerical Experiments ◽  
Random Environments ◽  
Logistic Growth ◽  
Small Diffusion ◽  
Stochastic Logistic Model ◽  
Diffusion Rates ◽  
Definition Of ◽  
Do So

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.

Sign in / Sign up

Export Citation Format

Share Document