Stability, Bifurcation, Chaos : Discrete Prey Predator Model with Step Size

,; Selvam*, A. George Maria; Janagaraj, R.; ,; Jacintha, Mary; ,

doi:10.35940/ijitee.a4866.119119

Cited by 5 publications

(2 citation statements)

References 6 publications

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“…If the change is discrete, it would be more appropriate to use difference equations for modelling. Moreover, these equations provide a more realistic approach to describe events with different characteristic processes, while retaining the essential properties of the corresponding continuous time models, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. For this purpose, we provide more recent articles as references [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Analyses of the SIR Epidemic Model Including Treatment and Immigration

Ak Gümüş,

Selvam,

Kılınç

et al. 2024

Journal of Mathematical Sciences and Modelling

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This paper aims to examine the dynamics of a variation of a nonlinear SIR epidemic model. We analyze the complex dynamic nature of the discrete time SIR epidemic model by discretizing a continuous SIR epidemic model subject to treatment and immigration effects with the Euler method. First of all, we show the existence of equilibrium points of the model by reducing the three-dimensional system to the two-dimensional system. Next, we show the stability conditions of the obtained positive equilibrium point and the visibility of Flip and Neimark-Sacker bifurcation. We also perform numerical simulations to support analytical results. We do all these analyzes for models with and without immigration; and shows the effect of immigration on dynamics.

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Section: Introductionmentioning

confidence: 99%

Analyses of the SIR Epidemic Model Including Treatment and Immigration

Ak Gümüş,

Selvam,

Kılınç

et al. 2024

Journal of Mathematical Sciences and Modelling

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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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