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

2020 ◽  
Vol 15 (3) ◽  
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.

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

2014 ◽  
Vol 955-959 ◽  
pp. 463-470
Author(s):  
Jing Liu ◽  
Hong Wei Jiang ◽  
Chao Liu
Keyword(s):  
Food Chain ◽  
Consumption Rate ◽  
Three Dimensional ◽  
Quadratic Function ◽  
Positive Equilibrium ◽  
Chain Model ◽  
Equilibrium Solutions ◽  
Existence And Stability ◽  
Variable Consumption ◽  
Food Chain Model

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.

scholarly journals SIS MODEL WITH HARVESTING IN FOOD CHAIN MODEL

2020 ◽  
Vol 25 (1) ◽  
pp. 108
Author(s):  
Sufyan A. Wuhaib ◽  
Bilal A. Yaseen
Keyword(s):  
Mathematical Model ◽  
Food Chain ◽  
Molecular System ◽  
Chain Model ◽  
Sis Model ◽  
Periodic Boundaries ◽  
The Stability ◽  
Food Chain Model ◽  
The Mathematical Model

The aim of this study the mathematical model of the type SIS, healthy prey is infected by disease and the study proved that solution and restrictive in which the molecular system do not have periodic boundaries, then it discussed the stability of those points. the study also showed how to control the disease using the harvest so as not to become an epidemic.   http://dx.doi.org/10.25130/tjps.25.2020.017

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.

Numerical solution of time-fractional three-species food chain model arising in the realm of mathematical ecology

2020 ◽  
Vol 13 (02) ◽  
pp. 2050011 ◽  
Author(s):  
Ved Prakash Dubey ◽  
Rajnesh Kumar ◽  
Devendra Kumar
Keyword(s):  
Fractional Order ◽  
Food Chain ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Time Derivative ◽  
Chain Model ◽  
Homotopy Analysis ◽  
Food Chain Model ◽  
Derivatives Of

This research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives. The offered technique is a fantastic blend of homotopy analysis method (HAM) and Laplace transform (LT) operator and has been used fruitfully in the numerical computation of various fractional differential equations (FDEs). This paper involves the fractional derivatives of Caputo style. The numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial conditions. It is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only — a fact which authenticates the easiness and soundness of the suggested hybrid scheme. The variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical presentations. The outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
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.

scholarly journals Chaotic Discrete Fractional-Order Food Chain Model and Hybrid Image Encryption Scheme Application

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 161
Author(s):  
Sameh Askar ◽  
Abdulrahman Al-khedhairi ◽  
Amr Elsonbaty ◽  
Abdelalim Elsadany
Keyword(s):  
Fractional Order ◽  
Food Chain ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
High Sensitivity ◽  
Phase Portraits ◽  
Chain Model ◽  
Encryption Scheme ◽  
Dynamical Behaviors ◽  
Food Chain Model

Using the discrete fractional calculus, a novel discrete fractional-order food chain model for the case of strong pressure on preys map is proposed. Dynamical behaviors of the model involving stability analysis of its equilibrium points, bifurcation diagrams and phase portraits are investigated. It is demonstrated that the model can exhibit a variety of dynamical behaviors including stable steady states, periodic and quasiperiodic dynamics. Then, a hybrid encryption scheme based on chaotic behavior of the model along with elliptic curve key exchange scheme is proposed for colored plain images. The hybrid scheme combines the characteristics of noise-like chaotic dynamics of the map, including high sensitivity to values of parameters, with the advantages of reliable elliptic curves-based encryption systems. Security analysis assures the efficiency of the proposed algorithm and validates its robustness and efficiency against possible types of attacks.

scholarly journals SIS MODEL WITH HARVESTING IN FOOD CHAIN MODEL

2020 ◽  
Vol 25 (2) ◽  
pp. 93
Author(s):  
, Bilal A. Yaseen
Keyword(s):  
Mathematical Model ◽  
Food Chain ◽  
Molecular System ◽  
Chain Model ◽  
Sis Model ◽  
Periodic Boundaries ◽  
The Stability ◽  
Food Chain Model ◽  
The Mathematical Model

The aim of this study the mathematical model of the type SIS , healthy prey is infected by disease and the study proved that solution and restrictive in which the molecular system do not have periodic boundaries , then it discussed the stability of those points. the study also showed how to control the disease using the harvest so as not to become an epidemic   http://dx.doi.org/10.25130/tjps.25.2020.035

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