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.

Dynamics of a three species ratio-dependent food chain model with intra-specific competition within the top predator

2017 ◽  
Vol 85 ◽  
pp. 63-74 ◽  
Author(s):  
Nijamuddin Ali ◽  
Mainul Haque ◽  
Ezio Venturino ◽  
Santabrata Chakravarty
Keyword(s):  
Food Chain ◽  
Chain Model ◽  
Top Predator ◽  
Ratio Dependent ◽  
Food Chain Model

scholarly journals ON NONLINEAR FRACTIONAL-ORDER MATHEMATICAL MODEL OF FOOD-CHAIN

Fractals ◽  
2021 ◽  
Author(s):  
KOTTAKKARAN SOOPPY NISAR ◽  
MATI UR RAHMAN ◽  
GHAYLEN LAOUINI ◽  
MESHAL SHUTAYWI ◽  
MUHAMMAD ARFAN
Keyword(s):  
Mathematical Model ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Order ◽  
Food Chain ◽  
Existence Results ◽  
Chain Model ◽  
Top Predator ◽  
The Fixed Point Theorem ◽  
Food Chain Model

This paper investigates the dynamical semi-analysis of the delayed food chain model under the considered fractional order. The food chain model is composed of three compartments, namely, population of the prey, intermediate predator and a top predator. By using the fixed point theorem approach, we exploit some conditions for existence results and stability for the considered system via Atangana–Baleanu–Caputo derivative with fractional order. Also, using the well-known Adam–Bashforth technique for numerics, we simulate the concerning results for the interference between the prey and intermediate predator. Graphical results are discussed for different fractional-order values for the considered model.

Sign in / Sign up

Export Citation Format

Share Document