Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system

Javidi, Mohammad; Ahmad, Bashir

doi:10.1016/j.ecolmodel.2015.06.016

Cited by 128 publications

(76 citation statements)

References 41 publications

(44 reference statements)

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“…If one takes the same parameters as in [9] which are used in figure 1 [9] which contradicts with the fact that the critical value α * must be in the interval ( ) 0,1 .…”

Section: Equilibrium Point and Stabilitymentioning

confidence: 89%

“…In [9], the authors introduced a fractional order phytoplankton toxic-phytoplankton zooplankton system and provide some numerical simulations. In [9,[24][25][26][27], the authors used a particular numerical scheme according to Atanackovic and Stankovich in [28,29].…”

Section: Resultsmentioning

confidence: 99%

“…Javidi [9] introduced the following theorem: Theorem 3.1. The equilibrium 4 E is locally asymptotically stable if…”

Section: Equilibrium Point and Stabilitymentioning

confidence: 99%

“…aH is the reproduction numbers while = 2 1 1 r R bH is the basic reproduction number, see [9]. The point 3 E exists if > T eP m…”

Section: Equilibrium Point and Stabilitymentioning

confidence: 99%

“…phytoplankton, toxic phytoplankton and zooplankton can be written as a set of three nonlinear fractional differential equations as follows [9]:…”

Section: Introductionmentioning

confidence: 99%

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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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“…If one takes the same parameters as in [9] which are used in figure 1 [9] which contradicts with the fact that the critical value α * must be in the interval ( ) 0,1 .…”

Section: Equilibrium Point and Stabilitymentioning

confidence: 89%

Section: Resultsmentioning

confidence: 99%

“…Javidi [9] introduced the following theorem: Theorem 3.1. The equilibrium 4 E is locally asymptotically stable if…”

Section: Equilibrium Point and Stabilitymentioning

confidence: 99%

“…aH is the reproduction numbers while = 2 1 1 r R bH is the basic reproduction number, see [9]. The point 3 E exists if > T eP m…”

Section: Equilibrium Point and Stabilitymentioning

confidence: 99%

“…phytoplankton, toxic phytoplankton and zooplankton can be written as a set of three nonlinear fractional differential equations as follows [9]:…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fractional Order Model of Phytoplankton-toxic Phytoplankton-Zooplankton System

El-Shahed¹,

Ahmed²,

Abdelstar³

2018

AAN

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Existence theory for a system of coupled multi‐term fractional differential equations with integral multi‐strip coupled boundary conditions

Ahmad

Alghamdi

Alsaedi

et al. 2019

Math Methods in App Sciences

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Mathematical and numerical analysis of a three‐species predator‐prey model with herd behavior and time fractional‐order derivative

Ghanbari

Djilali

2019

Math Methods in App Sciences

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In this paper, we investigate with a time fractional-order derivative in a three-species predator-prey model with the presence of prey social behavior. A new approximation for predator-prey interaction in the presence of prey social behavior has been considered. For the model analysis, the study has been divided into two principal parts. First of all, we study the local stability of the equilibria and the existence of Hopf bifurcation. Then, for the numerical analysis, the Caputo fractional derivative operator is utilized to approximate the numerical solution of the model. An excellent agreement is seen between the numerical results and the theoretical predictions. KEYWORDS fractional derivative, herd behavior, Hopf bifurcation, numerical schema, predator-prey model MSC CLASSIFICATION 26A33; 37N25; 74S30; 91B501) Math Meth Appl Sci. 2020;43:1736-1752. wileyonlinelibrary.com/journal/mma

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Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system

Cited by 128 publications

References 41 publications

Fractional Order Model of Phytoplankton-toxic Phytoplankton-Zooplankton System

Fractional Order Model of Phytoplankton-toxic Phytoplankton-Zooplankton System

Existence theory for a system of coupled multi‐term fractional differential equations with integral multi‐strip coupled boundary conditions

Mathematical and numerical analysis of a three‐species predator‐prey model with herd behavior and time fractional‐order derivative

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