Flip bifurcation and stability analysis of a fractional-order population dynamics with Allee effect

2019 ◽  
Vol 22 (6) ◽  
pp. 1009-1029 ◽  
Author(s):  
F. Bozkurt ◽  
A. Yousef
Keyword(s):  
Population Dynamics ◽  
Stability Analysis ◽  
Fractional Order ◽  
Allee Effect ◽  
Flip Bifurcation ◽  
Bifurcation And Stability

scholarly journals Bifurcation and Stability Analysis of a System of Fractional-Order Differential Equations for a Plant–Herbivore Model with Allee Effect

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 454 ◽  
Author(s):  
Ali Yousef ◽  
Fatma Bozkurt Yousef
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Order ◽  
Flip Bifurcation ◽  
Center Manifold Theorem ◽  
Fractional Order Differential Equations ◽  
Existence And Stability ◽  
Plant Herbivore Interaction ◽  
Plant Herbivore ◽  
Bifurcation And Stability

This article concerns establishing a system of fractional-order differential equations (FDEs) to model a plant–herbivore interaction. Firstly, we show that the model has non-negative solutions, and then we study the existence and stability analysis of the constructed model. To investigate the case according to a low population density of the plant population, we incorporate the Allee function into the model. Considering the center manifold theorem and bifurcation theory, we show that the model shows flip bifurcation. Finally, the simulation results agree with the theoretical studies.

Bifurcation and stability analysis of a discrete SIR epidemic model of fractional order

2022 ◽  
Author(s):  
A. George Maria Selvam ◽  
D. Abraham Vianny ◽  
S. Britto Jacob ◽  
D. Vignesh
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Bifurcation And Stability

scholarly journals Stability Analysis for a Fractional HIV Infection Model with Nonlinear Incidence

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Linli Zhang ◽  
Gang Huang ◽  
Anping Liu ◽  
Ruili Fan
Keyword(s):  
Population Dynamics ◽  
Stability Analysis ◽  
Hiv Infection ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Nonnegative Solution ◽  
Infection Model ◽  
Nonlinear Incidence ◽  
Hiv Infection Model ◽  
The Stability

We introduce the fractional-order derivatives into an HIV infection model with nonlinear incidence and show that the established model in this paper possesses nonnegative solution, as desired in any population dynamics. We also deal with the stability of the infection-free equilibrium, the immune-absence equilibrium, and the immune-presence equilibrium. Numerical simulations are carried out to illustrate the results.

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

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Agus Suryanto ◽  
Isnani Darti ◽  
Syaiful Anam
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Local Stability ◽  
Allee Effect ◽  
Dynamical Behavior ◽  
Continuous Model ◽  
Positivity Of Solutions ◽  
Existence Conditions ◽  
Dynamical Properties

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.

scholarly journals Stability Analysis of a Fractional-Order Leslie-Gower Model with Allee Effect in Predator

2021 ◽  
Vol 1821 (1) ◽  
pp. 012051
Author(s):  
Emli Rahmi ◽  
Isnani Darti ◽  
Agus Suryanto ◽  
Trisilowati ◽  
Hasan S. Panigoro
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Allee Effect
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