Dynamical behavior of fractional-order Hastings–Powell food chain model and its discretization

Matouk, A. E.; Elsadany, A. A.; Ahmed, E.; Agiza, H.N.

doi:10.1016/j.cnsns.2015.03.004

Cited by 96 publications

(51 citation statements)

References 46 publications

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“…For numerical solutions of system (2.1), one can use the generalized Adams-Bashforth-Moulton method. To give the approximate solution by means of this algorithm, consider the following nonlinear fractional-order differential equation [10,[14][15][16][17][18][19][20][21][22][23]: …”

Section: Numerical Methods and Simulationmentioning

confidence: 99%

Fractional Order Model of Phytoplankton-toxic Phytoplankton-Zooplankton System

El-Shahed¹,

Ahmed²,

Abdelstar³

2018

AAN

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Abstract. In this paper, a fractional-order model for phytoplankton-toxic phytoplanktonzooplankton system is presented. This model consists of three components: phytoplankton, toxic phytoplankton, and zooplankton. The equilibrium points are computed and stability of the equilibrium points is analyzed. In addition, fractional Hopf bifurcation conditions for the model are proposed. The generalized Adams-Bashforth-Moulton method is used to solve and simulate the system of fractional differential equations.

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Section: Numerical Methods and Simulationmentioning

confidence: 99%

Fractional Order Model of Phytoplankton-toxic Phytoplankton-Zooplankton System

El-Shahed¹,

Ahmed²,

Abdelstar³

2018

AAN

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“…In this research, the predatory-prey model [7] is the main object of the study. The model construction is done by modifying the model of Sahoo and Poria [2] by changing the integer order into the fractional-order.…”

Section: Model Formulationmentioning

confidence: 99%

“…Moreover, predator-prey food chains have been studied in structured populations in [5,6]. In this paper, Model is a modification of model [7]. Then the conditions of existence and stability of the equilibrium points of the fractional-order are examined in the result and discussion.…”

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confidence: 99%

Dynamical Analysis of Fractional-Order Hastings-Powell Food Chain Model with Alternative Food

Huda

Trisilowati

Suryanto

2017

JELS

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In this paper, a fractional-order Hastings-Powell food chain model is discussed. It is assumed that the top-predator population is supported by alternative food. Existence and local stability of equilibrium points of fractional-order system are investigated. Numerical simulations are conducted to illustrate analysis results. The analysis results show that alternative food can give a positive impact for top-predator population.

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“…Based on the Holling type II functional response, we know that the middle predator y feeds on the prey x and the top predator z preys upon y. We can write the three species food chain model as follows [12]:…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation analysis and its preliminary control in a Hasting-Powell food chain model with two different delays

Zhang¹,

Lu²,

Du³

et al. 2017

J. Nonlinear Sci. Appl.

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Keeping the balance of nature is important, and it is very significant to effectively control the number of species for ecosystem stability. In this paper, we propose a tritrophic Hastings-Powell (HP) model with two different time delays, and the local stability of equilibrium, Hopf bifurcation, and the existence and uniqueness of the positive equilibrium are analyzed in detail. Besides, we obtain the stable conditions for the system and prove that Hopf bifurcation will occur when the delay pass through the critical value. And the stability and direction of the Hopf bifurcation are also investigated by using the center manifold theorem and normal form theorem. Finally, some numerical examples are given to illustrate the results.

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Dynamical behavior of fractional-order Hastings–Powell food chain model and its discretization

Cited by 96 publications

References 46 publications

Fractional Order Model of Phytoplankton-toxic Phytoplankton-Zooplankton System

Fractional Order Model of Phytoplankton-toxic Phytoplankton-Zooplankton System

Dynamical Analysis of Fractional-Order Hastings-Powell Food Chain Model with Alternative Food

Hopf bifurcation analysis and its preliminary control in a Hasting-Powell food chain model with two different delays

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