Dynamic analysis of a fractional order prey–predator interaction with harvesting

Javidi, Mohammad; Nyamoradi, Nemat

doi:10.1016/j.apm.2013.04.024

Cited by 107 publications

(67 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [9,[24][25][26][27], the authors used a particular numerical scheme according to Atanackovic and Stankovich in [28,29]. This method is not proved to be convergent and deserves more study as already pointed out in [30].…”

Section: Resultsmentioning

confidence: 99%

Fractional Order Model of Phytoplankton-toxic Phytoplankton-Zooplankton System

El-Shahed¹,

Ahmed²,

Abdelstar³

2018

AAN

View full text Add to dashboard Cite

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.

show abstract

Section: Resultsmentioning

confidence: 99%

Fractional Order Model of Phytoplankton-toxic Phytoplankton-Zooplankton System

El-Shahed¹,

Ahmed²,

Abdelstar³

2018

AAN

View full text Add to dashboard Cite

show abstract

“…There are many applications of fractional‐order differential equations in the field of system biology, physics, chemistry and biochemistry, engineering, and medicine . Fractional‐order biological systems are studied in previous works …”

Section: Introductionmentioning

confidence: 99%

Study of a fractional‐order model of chronic wasting disease

2020

View full text Add to dashboard Cite

This paper studies a fractional‐order modelling chronic wasting disease (CWD). The basic results on existence, uniqueness, non‐negativity, and boundedness of the solutions are investigated for the considered model. The criterion for local as well as global stability of the equilibrium points is derived. A numerical analysis for Hopf‐type bifurcation is presented. Finally, numerical simulations are provided to justify the results obtained.

show abstract

“…With the rapid development of fractional calculus, fractional differential equations have been implemented in various fields including biological system. This is due the fact that fractional differential equations are naturally related to the real life phenomena with memory which exists in most of biological system [10][11][12][13][14][15][16]. To describe such memory effect, we first recall the definition of fractional integral operator as well as fractional differential operator.…”

Section: International Journal Of Mathematics and Mathematical Sciencesmentioning

confidence: 99%

Stability Analysis of a Fractional Order Modified Leslie-Gower Model with Additive Allee Effect

Suryanto

Darti

Anam

2017

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

We analyze the dynamics of a fractional order modified Leslie-Gower model with Beddington-DeAngelis functional response and additive Allee effect by means of local stability. In this respect, all possible equilibria and their existence conditions are determined and their stability properties are established. We also construct nonstandard numerical schemes based on Grünwald-Letnikov approximation. The constructed scheme is explicit and maintains the positivity of solutions. Using this scheme, we perform some numerical simulations to illustrate the dynamical behavior of the model. It is noticed that the nonstandard Grünwald-Letnikov scheme preserves the dynamical properties of the continuous model, while the classical scheme may fail to maintain those dynamical properties.

show abstract

Dynamic analysis of a fractional order prey–predator interaction with harvesting

Cited by 107 publications

References 30 publications

Fractional Order Model of Phytoplankton-toxic Phytoplankton-Zooplankton System

Fractional Order Model of Phytoplankton-toxic Phytoplankton-Zooplankton System

Study of a fractional‐order model of chronic wasting disease

Stability Analysis of a Fractional Order Modified Leslie-Gower Model with Additive Allee Effect

Contact Info

Product

Resources

About