Study on autonomous and nonautonomous version of a food chain model with intraspecific competition in top predator

2019 ◽  
Vol 43 (6) ◽  
pp. 3167-3184 ◽  
Author(s):  
Jyotirmoy Roy ◽  
Shariful Alam
Keyword(s):  
Food Chain ◽  
Intraspecific Competition ◽  
Chain Model ◽  
Top Predator ◽  
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.

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 Long time dynamics of a three-species food chain model with Allee effect in the top predator

2016 ◽  
Vol 71 (2) ◽  
pp. 503-528 ◽  
Author(s):  
Rana D. Parshad ◽  
Emmanuel Quansah ◽  
Kelly Black ◽  
Ranjit Kumar Upadhyay ◽  
S.K. Tiwari ◽  
...  
Keyword(s):  
Food Chain ◽  
Allee Effect ◽  
Chain Model ◽  
Top Predator ◽  
Time Dynamics ◽  
Long Time ◽  
Food Chain Model ◽  
Long Time Dynamics

The role of top predator interference on the dynamics of a food chain model

2013 ◽  
Vol 18 (3) ◽  
pp. 757-768 ◽  
Author(s):  
Ranjit Kumar Upadhyay ◽  
Raid Kamel Naji ◽  
Sharada Nandn Raw ◽  
Balram Dubey
Keyword(s):  
Food Chain ◽  
Chain Model ◽  
Top Predator ◽  
Predator Interference ◽  
Food Chain Model

scholarly journals Extinction of top-predator in a three-level food-chain model

1998 ◽  
Vol 37 (4) ◽  
pp. 372-380 ◽  
Author(s):  
Chuang-Hsiung Chiu ◽  
Sze-Bi Hsu
Keyword(s):  
Food Chain ◽  
Chain Model ◽  
Top Predator ◽  
Food Chain Model

scholarly journals Dynamical analysis of a delayed food chain model with additive Allee effect

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. Vinoth ◽  
R. Sivasamy ◽  
K. Sathiyanathan ◽  
Grienggrai Rajchakit ◽  
P. Hammachukiattikul ◽  
...  
Keyword(s):  
Food Chain ◽  
Allee Effect ◽  
Time Lag ◽  
Dynamical Analysis ◽  
Chain Model ◽  
Top Predator ◽  
Interior Equilibrium ◽  
Top Predators ◽  
Proposed Model ◽  
Food Chain Model

AbstractDynamical analysis of a delayed tri-trophic food chain consisting of prey, an intermediate, and a top predator is investigated in this paper. The additive Allee effect is introduced in the prey population, and it is assumed that there is a time lag due to the gestation effect in the intermediate predator. The interference among the prey and the intermediate predator is according to Holling type II, while the interaction between the intermediate and top predators follows the Crowley–Martin functional response. The local stability and bifurcation analysis of the proposed model at the interior equilibrium point are studied. Numerical simulations are provided to ensure the mathematical results.

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