scholarly journals Mathematical Modelling of Deforestation Due to Population Density and Industrialization

Jurnal Varian ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 9-16
Author(s):  
Didiharyono D. ◽  
Irwan Kasse
Keyword(s):  
Numerical Simulation ◽  
Population Density ◽  
Mathematical Modelling ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Stability Criteria ◽  
Hurwitz Stability ◽  
Stable Conditions ◽  
Linear Differential ◽  
The Stability

The focus of the study in this paper is to model deforestation due to population density and industrialization. To begin with, it is formulated into a mathematical modelling which is a system of non-linear differential equations. Then, analyze the stability of the system based on the Routh-Hurwitz stability criteria. Furthermore, a numerical simulation is performed to determine the shift of a system. The results of the analysis to shown that there are seven non-negative equilibrium points, which in general consist equilibrium point of disturbance-free and equilibrium points of disturbances. Equilibrium point TE7(x, y, z) analyzed to shown asymptotically stable conditions based on the Routh-Hurwitz stability criteria. The numerical simulation results show that if the stability conditions of a system have been met, the system movement always occurs around the equilibrium point.

scholarly journals Stability Analysis of Model tuberculosis Spread in Diabetes Mellitus Patients with Treatment Factors

2020 ◽  
Vol 17 (1) ◽  
pp. 50-60
Author(s):  
Nursamsi Nursamsi
Keyword(s):  
Diabetes Mellitus ◽  
Numerical Simulation ◽  
Stability Analysis ◽  
Equilibrium Point ◽  
Immune Function ◽  
Blood Sugar ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Sugar Levels ◽  
The Stability

Diabetes mellitus (Dm) is a disease associated with impaired immune function so it is more susceptible to get infections including Tuberculosis (Tb). Tb disease can also worsen blood sugar levels which can cause Dm disease. This study aims to analyze and determine the stability of the equilibrium point of the spread of Tb disease in patients with Dm with consideration nine compartments, which are susceptible Tb without Dm, susceptible Tb without Dm complication, susceptible Tb with Dm complication, expose Tb without Dm, expose Tb with Dm, infected Tb without Dm, infected Tb with Dm, recovered Tb without Dm, and recovered Tb with Dm with treatment factors. The result obtained from the analysis of the model is two equilibrium points, which are the non endemic and endemic equilibrium points. The endemic equilibrium point does not exist if , endemic will appear if . Analytical and numerical simulation show that the spread of disease can be reduced and stopped if treatment is given to the infected compartment.

DYNAMICAL ANALYSIS OF FRACTIONAL ORDER ZIKV MODEL

2021 ◽  
Vol 10 (5) ◽  
pp. 2469-2481
Author(s):  
N.A. Hidayati ◽  
A. Suryanto ◽  
W.M. Kusumawinahyu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Stability Conditions ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
S Model

The ZIKV model presented in this article is developed by modifying \cite{Bonyah2016}’s model. The classical order is changed into fractional order model. The equilibrium points of the model are determined and the stability conditions of each equilibrium point have been done using Routh-Hurwitz conditions. Numerical simulation is presented to verify the result of stability analysis result. Numerical simulation is also used to shows the effect of the order $\alpha$ to the stability of the model’s equilibrium point.

scholarly journals ANALISIS KESTABILAN MODEL INTERAKSI PREDATOR-PREY DENGAN FUNGSI RESPON MONOD-HALDANE DAN PERILAKU ANTI PEMANGSA

2020 ◽  
Vol 8 (2) ◽  
pp. 51-59
Author(s):  
Muhammad Bachtiar Gaib ◽  
Wahdania At. Ja'a
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Predator Prey ◽  
First Case ◽  
Point Determination ◽  
Predator Model ◽  
The Stability ◽  
Predator Behavior

This article examines a competing prey-predator model using the Monod-Haldane response function and anti-predator behavior. This article discusses equilibrium point determination, equilibrium point stability analysis, and numerical simulation. Obtained three equilibrium points, namely T1, T2, and T3, where the equilibrium-point is always saddle, the stability of the equilibrium points T2 and T3 will be stable if it meets the predetermined parameter requirements. There are two cases in the equilibrium point where the first case is vertically stable and the second case is spiral stable.

scholarly journals Equilibrium Further Studied for Combined System of Cournot and Bertrand: A Differential Approach

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Bingyuan Gao ◽  
Yueping Du
Keyword(s):  
General Equilibrium ◽  
Equilibrium Point ◽  
Price Competition ◽  
Dynamic Equilibrium ◽  
Equilibrium Points ◽  
Cournot Model ◽  
Combined System ◽  
Quantity Competition ◽  
Bertrand Model ◽  
The Stability

In general, quantity competition and price competition exist simultaneously in a dynamic economy system. Whether it is quantity competition or price competition, when there are more than three companies in one market, the equilibrium points will become chaotic and are very difficult to be derived. This paper considers generally dynamic equilibrium points of combination of the Bertrand model and Cournot model. We analyze general equilibrium points of the Bertrand model and Cournot model, respectively. A general equilibrium point of the combination of the Cournot model and Bertrand model is further investigated in two cases. The theory of spatial agglomeration and intermediate value theorem are introduced. In addition, the stability of equilibrium points is further illustrated on celestial bodies motion. The results show that at least a general equilibrium point exists in combination of Cournot and Bertrand. Numerical simulations are given to support the research results.

scholarly journals Stability and Bifurcation of a Prey-Predator-Scavenger Model in the Existence of Toxicant and Harvesting

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Huda Abdul Satar ◽  
Raid Kamel Naji
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Food Web ◽  
Equilibrium Points ◽  
Local Bifurcation ◽  
Persistence Conditions ◽  
Stability And Bifurcation ◽  
Periodic Dynamics ◽  
The Stability ◽  
Food Web Model

In this paper a prey-predator-scavenger food web model is proposed and studied. It is assumed that the model considered the effect of harvesting and all the species are infected by some toxicants released by some other species. The stability analysis of all possible equilibrium points is discussed. The persistence conditions of the system are established. The occurrence of local bifurcation around the equilibrium points is investigated. Numerical simulation is used and the obtained solution curves are drawn to illustrate the results of the model. Finally, the nonexistence of periodic dynamics is discussed analytically as well as numerically.

The Qualitative Analysis of Two Populations Commensalisms Model

2012 ◽  
Vol 524-527 ◽  
pp. 3705-3708
Author(s):  
Guang Cai Sun
Keyword(s):  
Qualitative Analysis ◽  
Equilibrium Point ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Mathematics Model ◽  
Stable Equilibrium Point ◽  
The Stability ◽  
Two Populations

This paper deals with the mathematics model of two populations Commensalisms symbiosis and the stability of all equilibrium points the system. It has given the conclusion that there is only one stable equilibrium point the system. This paper also elucidates the biology meaning of the model and its equilibrium points.

On the Dynamical Behavior of Three Species System with Time Delays

2011 ◽  
Vol 130-134 ◽  
pp. 1544-1546
Author(s):  
Dan Na Sun ◽  
Zi Ku Wu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Zero Point ◽  
The Stability ◽  
Population Equilibrium

A three species system with time delays was considered. Firstly, we got the system’s three population equilibrium point and shifted it to zero point through transformation. Secondly, we analyzed the stability of the system at the equilibrium point. We support our analytical findings with numerical simulation.

Harvesting Analysis of a Predator-Prey System with Functional Response

2013 ◽  
Vol 805-806 ◽  
pp. 1957-1961
Author(s):  
Ting Wu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Predator Prey ◽  
Optimal Harvesting Policy ◽  
Prey System ◽  
The Stability ◽  
Maximal Principle

In this paper, a predator-prey system with functional response is studied,and a set of sufficient conditions are obtained for the stability of equilibrium point of the system. Moreover, optimal harvesting policy is obtained by using the maximal principle,and numerical simulation is applied to illustrate the correctness.

scholarly journals A Four-Zone Model and Nonlinear Dynamic Analysis of Solution Multiplicity of Buoyancy Ventilation in Underground Building

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-24
Author(s):  
Yuxing Wang ◽  
Chunyu Wei
Keyword(s):  
Differential Equations ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Underground Structure ◽  
Unstable Equilibrium ◽  
Phase Portraits ◽  
Zone Model ◽  
Unstable Equilibrium Point ◽  
Index 2 ◽  
The Stability

The solution multiplicity of natural ventilation in buildings is very important to personnel safety and ventilation design. In this paper, a four-zone model of buoyancy ventilation in typical underground building is proposed. The underground structure is divided to four zones, a differential equation is established in each zone, and therefore, there are four differential equations in the underground structure. By solving and analyzing the equilibrium points and characteristic roots of the differential equations, we analyze the stability of three scenarios and obtain the criterions to determine the stability and existence of solutions for two scenarios. According to these criterions, the multiple steady states of buoyancy ventilation in any four-zone underground buildings for different stack height ratios and the strength ratios of the heat sources can be obtained. These criteria can be used to design buoyancy ventilation or natural exhaust ventilation systems in underground buildings. Compared with the two-zone model in (Liu et al. 2020), the results of the proposed four-zone model are more consistent with CFD results in (Liu et al. 2018). In addition, the results of proposed four-zone model are more specific and more detailed in the unstable equilibrium point interval. We find that the unstable equilibrium point interval is divided into two different subintervals corresponding to the saddle point of index 2 and the saddle focal equilibrium point of index 2, respectively. Finally, the phase portraits and vector field diagrams for the two scenarios are given.

STABILITY BOUNDARY CHARACTERIZATION OF NONLINEAR AUTONOMOUS DYNAMICAL SYSTEMS IN THE PRESENCE OF A SUPERCRITICAL HOPF EQUILIBRIUM POINT

2013 ◽  
Vol 23 (12) ◽  
pp. 1350196 ◽  
Author(s):  
JOSAPHAT R. R. GOUVEIA ◽  
FABÍOLO MORAES AMARAL ◽  
LUÍS F. C. ALBERTO
Keyword(s):  
Dynamical Systems ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Stability Boundary ◽  
Complete Characterization ◽  
Center Manifolds ◽  
The Stability ◽  
Hyperbolic Equilibrium ◽  
Autonomous Dynamical Systems

A complete characterization of the boundary of the stability region (or area of attraction) of nonlinear autonomous dynamical systems is developed admitting the existence of a particular type of nonhyperbolic equilibrium point on the stability boundary, the supercritical Hopf equilibrium point. Under a condition of transversality, it is shown that the stability boundary is comprised of all stable manifolds of the hyperbolic equilibrium points lying on the stability boundary union with the center-stable and\or center manifolds of the type-k, k ≥ 1, supercritical Hopf equilibrium points on the stability boundary.

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