Qualitative Analysis of Three-Dimensional Single Food-Chain Model with Variable Consumption Rate in Chemostat

The paper studies three-dimensional food-chain model with variable consumption rate in Chemostat. Assume the prey population's consumption rate of the nutrients is quadratic function, and the predator's consumption rate of the prey population is linear function. Use qualitative theory of ordinary differential equation to analyze the equilibrium solution of the model, especially the existence and stability of positive equilibrium solutions and Hopf bifurcation solutions. Finally,several numerical simulations illustrating the theoretical analysis are also given.

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Stability and Hopf Bifurcation of a Fractional-Order Food Chain Model With Disease and Two Delays

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4045683 ◽

2020 ◽

Vol 15 (3) ◽

Cited By ~ 1

Author(s):

Xinhe Wang ◽

Zhen Wang ◽

Xiao Shen

Keyword(s):

Fractional Order ◽

Food Chain ◽

Positive Equilibrium ◽

Chain Model ◽

Two Delays ◽

Existence Conditions ◽

Positive Equilibrium Point ◽

The Stability ◽

Food Chain Model ◽

Bifurcation And Stability

Abstract In this study, a fractional-order food chain model with disease and two delays is proposed. The existence conditions for a positive equilibrium point are given, and the stability conditions without the effects of delays are established. The effects of a single time delay and two time delays are discussed, the bifurcation and stability criteria are obtained, and the bifurcation points are calculated. To support the theoretical analysis, numerical simulations are presented.

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Global Stability for a Three-Species Food Chain Model in a Patchy Environment

Journal of Applied Mathematics ◽

10.1155/2014/314729 ◽

2014 ◽

Vol 2014 ◽

pp. 1-5 ◽

Cited By ~ 1

Author(s):

Hongli Li ◽

Yaolin Jiang ◽

Long Zhang ◽

Zhidong Teng

Keyword(s):

Food Chain ◽

Sufficient Conditions ◽

Coupled Systems ◽

Positive Equilibrium ◽

Chain Model ◽

Patchy Environment ◽

Globally Asymptotically Stable ◽

Predator Species ◽

Graph Theoretical Approach ◽

Food Chain Model

We investigate a three-species food chain model in a patchy environment where prey species, mid-level predator species, and top predator species can disperse amongndifferent patches(n≥2). By using the method of constructing Lyapunov functions based on graph-theoretical approach for coupled systems, we derive sufficient conditions under which the positive equilibrium of this model is unique and globally asymptotically stable if it exists.

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Stability and Bifurcation Analysis in a Food Chain Model with Delay

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.110-116.3382 ◽

2011 ◽

Vol 110-116 ◽

pp. 3382-3388

Author(s):

Zhang Li

Keyword(s):

Hopf Bifurcation ◽

Food Chain ◽

Center Manifold ◽

Chain Model ◽

Center Manifold Theory ◽

Stability And Bifurcation Analysis ◽

Existence And Stability ◽

The Stability ◽

Manifold Theory ◽

Food Chain Model

In this paper, we investigate a delayed three-species food chain model. The existence and stability of equilibria are obtained. A explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory.

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