A nonstandard numerical scheme for a predator-prey model with Allee effect

Ongun, Mevlüde Yakit; ÖZDOĞAN, Nihal

doi:10.22436/jnsa.010.02.32

Cited by 9 publications

(7 citation statements)

References 23 publications

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“…where 𝜑𝜑(ℎ) depends on the step size ∆𝑡𝑡 = ℎ and it is called denominator function. It can be seen that how to find arbitrary choice of denominator functions in [24,25,26,27,31]. Let us indicate ℎ 1 = 𝜑𝜑(ℎ).…”

Section: Stability and Existence Analysis Of The Equilibrium Pointsmentioning

confidence: 99%

“…The most disadvantage of these methods are that their stability depends on the time step size. Whereas, nonstandard finite difference scheme preserves local stability of the equilibrium with arbitrary time step sizes [26]. By using nonstandard finite difference scheme, the arbitrary step size selection simplifys the solution of the problem [27].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical Behaviours of a Discretized Model With Michaelis-Menten Harvesting Rate

ÖZDOĞAN

Ongun

2022

Journal of Universal Mathematics

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In this paper, we introduced nonstandard finite difference scheme (NSFD) for solving the continuos model with Michaelis-Menten harvesting rate. We have seen that the proposed scheme preserve local stability and positivity. Stability analysis of each fixed point of the discrete time model has been proven. Also, numerical comparisons were made between the nonstandard finite difference method and the other methods.

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Section: Stability and Existence Analysis Of The Equilibrium Pointsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamical Behaviours of a Discretized Model With Michaelis-Menten Harvesting Rate

ÖZDOĞAN

Ongun

2022

Journal of Universal Mathematics

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“…where, J and trJ denote the coefficient matrix and the trace of the matrix of the linearized systems, respectively. These are some suggestions about Schur-Cohn criteria and its use [29,[34][35][36][37][38][39][40][41][42]. ( (…”

Section: Stability Analysismentioning

confidence: 99%

Nonstandard Finite Difference Scheme for a Computer Virus Model

Kocabiyik¹,

ÖZDOĞAN²,

Ongun³

2020

Journal of Innovative Science and Engineering (JISE)

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This study introduces us to a new model developed for computer viruses. The model is presented to remove the protective restriction on the total number of computers connected to the Internet. This model is nonlinear differential equation system. Therefore, finding analytical solutions is very difficult. This means that we have to apply numerical methods in order to find the solution. The behavior of numerical solution has been investigated for the discretized system. By using Nonstandard Finite Difference Scheme (NSFD), it is aimed to preserve both the positivity of the solutions for positive initial points and the local asymptotic stability of the equilibrium point.

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“…Furthermore, Moghadas et al [48] implemented nonstandard numerical scheme to analyze a Gause-type Lotka-Volterra model in generalized form. For more detail related to application of NSFD methods we refer to the study done by authors [34,38,39,49].…”

Section: Introductionmentioning

confidence: 99%

A Ratio-Dependent Nonlinear Predator-Prey Model With Certain Dynamical Results

et al. 2020

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In order to see the dynamics of prey-predator interaction, differential or difference equations are frequently used for modeling of such interactions. In present manuscript, we explore some qualitative aspects of two-dimensional ratio-dependent predator-prey model. Taking into account the non-overlapping generations for class of predator-prey system, a novel consistency preserving scheme is proposed. Our study reveals that the implemented discretization is bifurcation preserving. Some dynamical aspects including local behavior of equilibria, phase-plane analysis and emergence of Hopf bifurcation for continuous predator-prey model are studied. Moreover, existence of biologically feasible fixed points, their local asymptotic behavior and phase-plane classification of interior (positive) fixed point are carried out. Furthermore, bifurcation theory of normal forms is implemented to prove that proposed discrete-time model undergoes Neimark-Sacker bifurcation around its unique positive fixed point. Taking into account the bifurcating and fluctuating behaviour of discrete system, three chaos control strategies are implemented. Numerical simulations are provided to illustrate the theoretical discussion and effectiveness of introduced chaos control methods. INDEX TERMS Prey-predator interaction; stability analysis; Neimark-Sacker bifurcation; chaos control.

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A nonstandard numerical scheme for a predator-prey model with Allee effect

Cited by 9 publications

References 23 publications

Dynamical Behaviours of a Discretized Model With Michaelis-Menten Harvesting Rate

Dynamical Behaviours of a Discretized Model With Michaelis-Menten Harvesting Rate

Nonstandard Finite Difference Scheme for a Computer Virus Model

A Ratio-Dependent Nonlinear Predator-Prey Model With Certain Dynamical Results

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