scholarly journals On Dynamic Investigations of Cournot Duopoly Game: When Firms Want to Maximize Their Relative Profits

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2235
Author(s):  
Sameh Askar
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Utility Function ◽  
Global Analysis ◽  
Asymmetric Structure ◽  
Two Dimensional ◽  
Cournot Duopoly ◽  
The Stability ◽  
Nash Point ◽  
Discrete Map

This paper studies a Cournot duopoly game in which firms produce homogeneous goods and adopt a bounded rationality rule for updating productions. The firms are characterized by an isoelastic demand that is derived from a simple quadratic utility function with linear total costs. The two competing firms in this game seek the optimal quantities of their production by maximizing their relative profits. The model describing the game’s evolution is a two-dimensional nonlinear discrete map and has only one equilibrium point, which is a Nash point. The stability of this point is discussed and it is found that it loses its stability by two different ways, through flip and Neimark–Sacker bifurcations. Because of the asymmetric structure of the map due to different parameters, we show by means of global analysis and numerical simulation that the nonlinear, noninvertible map describing the game’s evolution can give rise to many important coexisting stable attractors (multistability). Analytically, some investigations are performed and prove the existence of areas known in literature with lobes.

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.

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 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 Investigations of Nonlinear Triopoly Models with Different Mechanisms

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
S. S. Askar ◽  
A. Al-khedhairi
Keyword(s):  
Dynamical System ◽  
Global Analysis ◽  
Discrete Dynamical System ◽  
The Other ◽  
3 Dimensional ◽  
Heterogeneous Players ◽  
State Point ◽  
The Stability ◽  
The Impact ◽  
Nash Point

This paper studies the dynamic characteristics of triopoly models that are constructed based on a 3-dimensional Cobb–Douglas utility function. The paper presents two parts. The first part introduces a competition among three rational firms on which their prices are isoelastic functions. The competition is described by a 3-dimensional discrete dynamical system. We examine the impact of rationality on the system’s steady state point. Studying the stability/instability of this point, which is Nash equilibrium and is unique in those models, is illustrated. Numerically, we give some global analysis of Nash point and its stability. The second part deals with heterogeneous scenarios. It consists of two different models. In the first model, we assume that one competitor adopts the local monopolistic approximation mechanism (LMA) while the other opponents are rational. The second model assumes two heterogeneous players with LMA mechanism against one rational firm. Studies show that the stability of NE point of those models is not guaranteed. Furthermore, simulation shows that when firms behave rational with symmetric costs, the stability of NE point is achievable.

Analysis and direct numerical simulation of the flow at a gravity-current head. Part 2. The lobe-and-cleft instability

2000 ◽  
Vol 418 ◽  
pp. 213-229 ◽  
Author(s):  
CARLOS HÄRTEL ◽  
FREDRIK CARLSSON ◽  
MATTIAS THUNBLOM
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Direct Numerical Simulation ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Gravity Current ◽  
Leading Edge ◽  
Two Dimensional ◽  
Amplification Rate ◽  
The Stability

Results are presented from a linear-stability analysis of the flow at the head of two-dimensional gravity-current fronts. The analysis was undertaken in order to clarify the instability mechanism that leads to the formation of the complex lobe-and-cleft pattern which is commonly observed at the leading edge of gravity currents propagating along solid boundaries. The stability analysis concentrates on the foremost part of the front, and is based on direct numerical simulation data of two-dimensional lock-exchange flows which are described in the companion paper, Härtel et al. (2000). High-order compact finite differences are employed to discretize the stability equations which results in an algebraic eigenvalue problem for the amplification rate, that is solved in an iterative fashion. The analysis reveals the existence of a vigorous linear instability that acts in a localized way at the leading edge of the front and originates in an unstable stratification in the flow region between the nose and stagnation point. It is shown that the amplification rate of this instability as well as its spanwise length scale depend strongly on Reynolds number. For validation, three-dimensional direct numerical simulations of the early stages of the frontal instability are performed, and close agreement with the results from the linear-stability analysis is demonstrated.

Spatiotemporal Dynamics of Phytoplankton-Fish System with the Allee Effect and Harvest Effect

2013 ◽  
Vol 726-731 ◽  
pp. 1604-1610
Author(s):  
Wei Wei Zhang ◽  
Min Zhao
Keyword(s):  
Numerical Simulation ◽  
Numerical Analysis ◽  
Pattern Formation ◽  
Equilibrium Point ◽  
Allee Effect ◽  
Spatiotemporal Dynamics ◽  
The Stability ◽  
Fish Interactions

In this paper, spatiotemporal dynamics of a phytoplankton-fish system with the Allee effect and harvest effect are investigated mathematically and numerically. Mathematical theoretical works have been pursued for the investigation of the stability of the equilibrium point of the phytoplankton-fish system with the Allee effect and harvest effect, which in turn provide a theoretical basic for the numerical simulation. Numerical analysis works indicate that Allee effect and harvest effect have a strong effect on the spatiotemporal dynamics of the phytoplankton-fish system using pattern formation. These results may help us to better understand phytoplankton-fish interactions.

Numerical Simulation of the Crack Propagation Processes in Rocks with Double Joints

2011 ◽  
Vol 90-93 ◽  
pp. 559-564 ◽  
Author(s):  
Jin Wei Fu ◽  
Wei Shen Zhu ◽  
Li Ge Wang ◽  
Xiang Gang Wang
Keyword(s):  
Numerical Simulation ◽  
Rock Mass ◽  
Crack Initiation ◽  
Rock Specimen ◽  
Failure Process ◽  
Jointed Rock ◽  
Two Dimensional ◽  
Analysis Software ◽  
Strength And Stiffness ◽  
The Stability

Engineering rock mass is commonly a brittle medium containing lots of joints or fissures. Under the stress redistribution in construction，the crack initiation，propagation，and coalescence may cause the strength and stiffness degradation of such medium. And these have an important impact on the stability of rock mass. By employing the analysis software of FLAC3D and improving the constitutive relation, the failure process of the double-cracked rock specimen under uniaxial and two-dimensional compression are simulated and studied. The numerical results match well with the testing results obtained by former scholars. The strength envelope of the jointed rock is obtained as well, and it is applied to analyzing the stability of a slope project.

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