scholarly journals Rich dynamics of a food chain model with ratio-dependent type III functional responses

2018 ◽  
Vol 5 (3) ◽  
pp. 124
Author(s):  
Manju Agarwal ◽  
Vimlesh Singh
Keyword(s):  
Food Chain ◽  
Chain Model ◽  
Functional Responses ◽  
Type Iii ◽  
Ratio Dependent ◽  
Food Chain Model ◽  
Dependent Type

scholarly journals Dynamics of a food chain model with ratio-dependent and modified Leslie-Gower functional responses

2015 ◽  
Vol 20 (7) ◽  
pp. 2269-2290 ◽  
Author(s):  
Wen-Bin Yang ◽  
◽  
Yan-Ling Li ◽  
Jianhua Wu ◽  
Hai-Xia Li ◽  
...  
Keyword(s):  
Food Chain ◽  
Chain Model ◽  
Functional Responses ◽  
Ratio Dependent ◽  
Food Chain Model

scholarly journals Effect of Time-Delay on a Ratio-Dependent Food Chain Model

2009 ◽  
Vol 14 (2) ◽  
pp. 199-216 ◽  
Author(s):  
B. Patra ◽  
A. Maiti ◽  
G. P. Samanta
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Food Chain ◽  
Chain Model ◽  
Functional Responses ◽  
Simple Criterion ◽  
Delayed System ◽  
Ratio Dependent ◽  
Food Chain Model ◽  
Practical Implications

This paper aims to study the effect of time-delay on a tritrophic food chainmodel with Michaelis-Menten type ratio-dependent functional responses. Boundednessof the time-delayed system is established. A simple criterion for deterministic extinctionis derived. It has been shown that the time-delay may introduce instability in the systemthrough Hopf bifurcation. Computer simulations are carried out to explain the analyticalfindings. It is discussed how these ideas illuminate some of the observed properties ofreal populations in the field, and explores practical implications.

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.

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