Impact of Dispersion on Dynamics of a Discrete Metapopulation Model

2007 ◽  
Vol 14 (04) ◽  
pp. 379-396 ◽  
Author(s):  
Yu Huang ◽  
Xingfu Zou
Keyword(s):  
Periodic Orbit ◽  
Discrete Time ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Metapopulation Model ◽  
Time Model ◽  
Discrete Time Model ◽  
Global Extinction ◽  
Dispersion Terms ◽  
The Impact

We propose and analyze a discrete time model for metapopulation on two patches with local logistic dynamics. The model carries a delay in the dispersion terms, and our results on this model show that the impact of the dispersion on the global dynamics of the metapopulation is complicated and interesting: it can affect the existence of a positive equilibrium; it can either drive the metapopulation to global extinction, or prevent the metapopulation from going to global extinction and stabilize a positive equilibrium; it can also destabilize a positive equilibrium or a periodic orbit.

Bifurcations and chaos control in a discrete-time biological model

2020 ◽  
Vol 13 (04) ◽  
pp. 2050022 ◽  
Author(s):  
A. Q. Khan ◽  
T. Khalique
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Control Method ◽  
Complex Dynamics ◽  
Small Neighborhood ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Flip Bifurcation ◽  
Time Model ◽  
Predator Prey Model

In this paper, bifurcations and chaos control in a discrete-time Lotka–Volterra predator–prey model have been studied in quadrant-[Formula: see text]. It is shown that for all parametric values, model has boundary equilibria: [Formula: see text], and the unique positive equilibrium point: [Formula: see text] if [Formula: see text]. By Linearization method, we explored the local dynamics along with different topological classifications about equilibria. We also explored the boundedness of positive solution, global dynamics, and existence of prime-period and periodic points of the model. It is explored that flip bifurcation occurs about boundary equilibria: [Formula: see text], and also there exists a flip bifurcation when parameters of the discrete-time model vary in a small neighborhood of [Formula: see text]. Further, it is also explored that about [Formula: see text] the model undergoes a N–S bifurcation, and meanwhile a stable close invariant curves appears. From the perspective of biology, these curves imply that between predator and prey populations, there exist periodic or quasi-periodic oscillations. Some simulations are presented to illustrate not only main results but also reveals the complex dynamics such as the orbits of period-2,3,13,15,17 and 23. The Maximum Lyapunov exponents as well as fractal dimension are computed numerically to justify the chaotic behaviors in the model. Finally, feedback control method is applied to stabilize chaos existing in the model.

Government Debt, Taxes and Growth

2000 ◽  
Vol 18 (2) ◽  
pp. 119-130
Author(s):  
Riccardo Fiorito
Keyword(s):  
Standard Model ◽  
Discrete Time ◽  
Government Debt ◽  
Tax Rates ◽  
Time Model ◽  
Discrete Time Model ◽  
Distortionary Taxation ◽  
The Standard Model ◽  
The Government ◽  
The Impact

Abstract By using a small discrete-time model we evaluate the impact of distortionary taxation on the government debt-to-GDP ratio. Once the standard model is modified accordingly, it appears that the increase of taxation has a growth cost which increases as long as die debt-to-GDP ratio rises. The empirical implementation uses data drawn from recent Italy’s record and is based on realistic shocks to the relevant parameters. A major finding is the importance of the debt level - not only of the dynamics - to stabilize the debt-to-GDP ratio. A second finding is that sustainable tax rates are remarkably lower than those prevailing in Italy since the 80s.

scholarly journals Supercritical Neimark–Sacker Bifurcation and Hybrid Control in a Discrete-Time Glycolytic Oscillator Model

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
A. Q. Khan ◽  
E. Abdullah ◽  
Tarek F. Ibrahim
Keyword(s):  
Discrete Time ◽  
Hybrid Control ◽  
Oscillator Model ◽  
Positive Equilibrium ◽  
Time Model ◽  
Discrete Time Model ◽  
Prime Period ◽  
Dynamical Properties ◽  
Positive Equilibrium Point ◽  
Theoretical Results

We study the local dynamical properties, Neimark–Sacker bifurcation, and hybrid control in a glycolytic oscillator model in the interior of ℝ+2. It is proved that, for all parametric values, Pxy+α/β+α2,α is the unique positive equilibrium point of the glycolytic oscillator model. Further local dynamical properties along with different topological classifications about the equilibrium Pxy+α/β+α2,α have been investigated by employing the method of linearization. Existence of prime period and periodic points of the model under consideration are also investigated. It is proved that, about the fixed point Pxy+α/β+α2,α, the discrete-time glycolytic oscillator model undergoes no bifurcation, except Neimark–Sacker bifurcation. A further hybrid control strategy is applied to control Neimark–Sacker bifurcation in the discrete-time model. Finally, theoretical results are verified numerically.

scholarly journals A New Simple Epidemic Discrete-Time Model Describing the Dissemination of Information with Optimal Control Strategy

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Hamza Boutayeb ◽  
Sara Bidah ◽  
Omar Zakary ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Control Strategy ◽  
Unstable State ◽  
Optimal Control Strategy ◽  
Time Model ◽  
Discrete Time Model ◽  
Before And After ◽  
The Impact ◽  
Information Amount

In this paper, we consider a new discrete-time model that describes the spread of information by sharing in some kind of online environments such as Facebook, WhatsApp, and Twitter. The impact of sharing on the information amount is investigated, which is incorporated in the considered model as a supplement compartment. We consider the possible interactions between individuals and information on the Internet, such as posts, images, and videos. The theory of control is used to show the effectiveness of our optimal control strategy in reducing the information amount and sharers and then decreases the dissemination of false information that can lead to annoying situations and unstable state in the society. Numerical simulations are performed to investigate several scenarios before and after the use of our strategy of control. Furthermore, sensitivity analysis of the information amount on parameters is simulated and discussed.

Non-homogeneous infinitely many sites discrete-time model with exact coalescent

2009 ◽  
Vol 33 (6) ◽  
pp. 713-732
Author(s):  
Adam Bobrowski ◽  
Marek Kimmel ◽  
Małgorzata Kubalińska
Keyword(s):  
Discrete Time ◽  
Time Model ◽  
Discrete Time Model
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