Neimark–Sacker Bifurcation of a Two-Dimensional Discrete-Time Chemical Model

Khan, A. Q.

doi:10.1155/2020/3936242

Cited by 6 publications

(8 citation statements)

References 14 publications

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“…Lemma 2.2. [15,17,22,34] Assume F (λ) = λ 2 + Bλ + C, where B and C are two real constants and let F (1) > 0. Suppose λ 1 and λ 2 are two roots of F (λ) = 0.…”

Section: Stability Analysis and Fixed Points Of The Systemmentioning

confidence: 99%

Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system

Kangalgil

Işık

2020

Hacettepe Journal of Mathematics and Statistics

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This article is about a discrete-time predator-prey model obtained by the forward Euler method. The stability of the fixed point of the model and the existence conditions of the Neimark-Sacker bifurcation are investigated. In addition, the direction of the Neimark-Sacker bifurcation is given. Moreover, OGY control method is to implement to control chaos caused by the Neimark-Sacker bifurcation. Finally, Neimark-Sacker bifurcation, chaos control strategy, and asymptotic stability of the only positive fixed point are verified with the help of numerical simulations. The existence of chaotic behavior in the model is confirmed by computing of the maximum Lyapunov exponents.

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“…Lemma 2.2. [15,17,22,34] Assume F (λ) = λ 2 + Bλ + C, where B and C are two real constants and let F (1) > 0. Suppose λ 1 and λ 2 are two roots of F (λ) = 0.…”

Section: Stability Analysis and Fixed Points Of The Systemmentioning

confidence: 99%

Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system

Kangalgil

Işık

2020

Hacettepe Journal of Mathematics and Statistics

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“…The results of their study show that the system exhibits abundant dynamical behaviors and the chemical reaction in the reactor will be in balance in the end under certain conditions. Khan [22], in his paper, studied the local dynamics and Neimark-Sacker bifurcation of a two-dimensional glycolytic oscillator model. It was found that the model has a unique equilibrium point for all α and β.…”

Section: Introductionmentioning

confidence: 99%

“…Further, we calculate the critical coefficients of each bifurcation. The two-dimensional discrete-time chemical model under consideration is given as follows [22]…”

Section: Introductionmentioning

confidence: 99%

Flip and generalized flip bifurcations of a two-dimensional discrete-time chemical model

Naik

Eskandari

Shahraki

2021

mmnsa

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This paper focuses on introducing a two-dimensional discrete-time chemical model and the existence of its fixed points. Also, the one and two-parameter bifurcations of the model are investigated. Bifurcation analysis is based on numerical normal forms. The flip (period-doubling) and generalized flip bifurcations are detected for this model. The critical coefficients identify the scenario associated with each bifurcation. To confirm the analytical results, we use the MATLAB package MatContM, which performs based on the numerical continuation method. Finally, bifurcation diagrams are presented to confirm the existence of flip (period-doubling) and generalized flip bifurcations for the glycolytic oscillator model that gives a better representation of the study.

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“…See [12] and references therein for examples of fitting parameters of models. Some most recent applications of Neimark-Sacker bifurcation for differential equations can be found in [13] and for difference equations in [14]. Some global asymptotic results for second order difference equations related to the results from [10], which will be used in the present paper, can be found in [15].…”

Section: Introductionmentioning

confidence: 99%

The Neimark–Sacker Bifurcation and Global Stability of Perturbation of Sigmoid Beverton–Holt Difference Equation

Kulenović

O’Loughlin

Pilav

2021

Discrete Dynamics in Nature and Society

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We present the bifurcation results for the difference equation x n + 1 = x n 2 / a x n 2 + x n − 1 2 + f where a and f are positive numbers and the initial conditions x − 1 and x 0 are nonnegative numbers. This difference equation is one of the perturbations of the sigmoid Beverton–Holt difference equation, which is a major mathematical model in population dynamics. We will show that this difference equation exhibits transcritical and Neimark–Sacker bifurcations but not flip (period-doubling) bifurcation since this difference equation cannot have period-two solutions. Furthermore, we give the asymptotic approximation of the invariant manifolds, stable, unstable, and center manifolds of the equilibrium solutions. We give the necessary and sufficient conditions for global asymptotic stability of the zero equilibrium as well as sufficient conditions for global asymptotic stability of the positive equilibrium.

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Neimark–Sacker Bifurcation of a Two-Dimensional Discrete-Time Chemical Model

Cited by 6 publications

References 14 publications

Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system

Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system

Flip and generalized flip bifurcations of a two-dimensional discrete-time chemical model

The Neimark–Sacker Bifurcation and Global Stability of Perturbation of Sigmoid Beverton–Holt Difference Equation

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