Stability Analysis and Controlling Chaos of Fractional-Order Three-Species Food Chain Model with Fear

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.

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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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Stability analysis of a three species food chain model with linear functional response via imprecise and parametric approach

Journal of Computational Science ◽

10.1016/j.jocs.2021.101423 ◽

2021 ◽

Author(s):

Uttam Ghosh ◽

Bapin Mondal ◽

Md Sadikur Rahman ◽

Susmita Sarkar

Keyword(s):

Stability Analysis ◽

Functional Response ◽

Food Chain ◽

Linear Functional ◽

Chain Model ◽

Parametric Approach ◽

Food Chain Model

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

International Journal of Biomathematics ◽

10.1142/s1793524520500114 ◽

2020 ◽

Vol 13 (02) ◽

pp. 2050011 ◽

Cited By ~ 3

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.

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

Symmetry ◽

10.3390/sym13020161 ◽

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.

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