Permanence and extinction of a three-species ratio-dependent food chain model with delay and prey diffusion

2010 ◽  
Vol 217 (5) ◽  
pp. 1825-1830 ◽  
Author(s):  
Chunxia Shen ◽  
Minsheng You
Keyword(s):  
Food Chain ◽  
Chain Model ◽  
Ratio Dependent ◽  
Food Chain Model

scholarly journals Dynamics of a three species ratio-dependent food chain model with diffusion and double free boundaries

2020 ◽  
Vol 15 ◽  
pp. 62
Author(s):  
Dawei Zhang ◽  
Beiping Duan ◽  
Binxiang Dai
Keyword(s):  
Food Chain ◽  
Dimensional Space ◽  
Chain Model ◽  
Time Behavior ◽  
Free Boundaries ◽  
Top Predator ◽  
Predator Species ◽  
Spreading And Vanishing ◽  
Ratio Dependent ◽  
Food Chain Model

This paper focuses on the dynamics of a three species ratio-dependent food chain model with diffusion and double free boundaries in one dimensional space, in which the free boundaries represent expanding fronts of top predator species. The existence, uniqueness and estimates of the global solution are discussed firstly. Then we prove a spreading–vanishing dichotomy, specifically, the top predator species either successfully spreads to the entire space as time t goes to infinity and survives in the new environment, or fails to establish and dies out in the long run. The long time behavior of the three species and criteria for spreading and vanishing are also obtained. Besides, our simulations illustrate the impacts of initial occupying area and expanding capability on the dynamics of top predator for free boundaries.

scholarly journals Erratum: Stationary Pattern of a Ratio-Dependent Food Chain Model with Diffusion

2009 ◽  
Vol 70 (1) ◽  
pp. 368-368 ◽  
Author(s):  
Rui Peng ◽  
Junping Shi ◽  
Mingxin Wang
Keyword(s):  
Food Chain ◽  
Chain Model ◽  
Stationary Pattern ◽  
Ratio Dependent ◽  
Food Chain Model
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