Allee effect and Holling type - II response in a discrete fractional order prey - predator model

Selvam, A. George Maria; Janagaraj, R.; Vignesh, D.

doi:10.1088/1742-6596/1139/1/012003

Cited by 9 publications

(2 citation statements)

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“…For example, Elsadany and Matouk [27] perform a numerical study through a discretization using the Euler method for the fractional-order Lotka-Volterra model. Also, using the same ideas, Selvam et al [28] studied a model fractional predator-prey with Holling type II functional response. Furthermore, for a fractional order Lotka-Volterra model, Jafari et al [29] obtained numerical solutions applying three-step Adams-Bashforth scheme and Das and Gupta [30] find an analytical solution using the homotopy perturbation method.…”

Section: Introductionmentioning

confidence: 99%

Fractional Lotka–Volterra model with Holling type III functional response

Catalan‐Angeles

Arciga-Alejandre

Sanchez-Ortiz

2023

Math Methods in App Sciences

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In this paper, we study a generalization of a Lotka–Volterra system with Holling type III functional response, where the Caputo fractional derivative is considered. Applying a multistage homotopy perturbation method, we obtain an analytical solution for the system. Moreover, analyzing the eigenvalues of the Jacobian matrix around the equilibria, we find sufficient conditions in order to guarantee the local stability and we present several examples to illustrate the behavior of solutions.

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Section: Introductionmentioning

confidence: 99%

Fractional Lotka–Volterra model with Holling type III functional response

Catalan‐Angeles

Arciga-Alejandre

Sanchez-Ortiz

2023

Math Methods in App Sciences

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“…In construction of biological models, fractional calculus relates the memory effects of biological populations very well rather than ordinary integer order calculus. Recently, models of species interaction and biological populations are developed using fractional calculus with discrete time [2,21,22,24,25].…”

Section: Introductionmentioning

confidence: 99%

Discretization and chaos control in a fractional order predator-prey harvesting model

Selvam¹,

Janagaraj²,

Vignesh³

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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The study of interaction between predator and prey species is one of the important subjects in mathematical biology. Optimal strategy control plays a vital role in preserving animals from extinction. Harvesting of species is a vital issue for the conservation biologists. In this work, we investigate the bifurcation and chaos control of the two species interaction model of fractional order in discrete time with harvesting of both prey and predator species. Existence results and the stability conditions of the system are analyzed using the fixed points and jacobian matrix. The chaotic behavior of the system is discussed with bifurcation diagrams. Linear control and hybrid control methods are used in controlling the chaos of the system. Numerical experiments with different phase portraits are simulated for the better understanding of the qualitative behavior of the considered model.

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