scholarly journals Dynamics of a Cournot Duopoly Game with a Generalized Bounded Rationality

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
A. Al-khedhairi
Keyword(s):  
Stability Analysis ◽  
Bounded Rationality ◽  
Numerical Computation ◽  
Local Stability ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Cournot Duopoly ◽  
Local Stability Analysis

In this paper, the dynamics of Cournot duopoly game with a generalized bounded rationality is considered. The fractional bounded rationality of the Cournot duopoly game is introduced. The conditions of local stability analysis of equilibrium points of the game are derived. The effect of fractional marginal profit on the game is investigated. The complex dynamics behaviors of the game are discussed by numerical computation when parameters are varied.

scholarly journals A Mathematical Model to Study the Effectiveness of Some of the Strategies Adopted in Curtailing the Spread of COVID-19

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Isa Abdullahi Baba ◽  
Bashir Abdullahi Baba ◽  
Parvaneh Esmaili
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Government Policy ◽  
Local Stability ◽  
Equilibrium Points ◽  
Compartmental Models ◽  
Effective Strategy ◽  
Local Stability Analysis ◽  
The Government

In this paper, we developed a model that suggests the use of robots in identifying COVID-19-positive patients and which studied the effectiveness of the government policy of prohibiting migration of individuals into their countries especially from those countries that were known to have COVID-19 epidemic. Two compartmental models consisting of two equations each were constructed. The models studied the use of robots for the identification of COVID-19-positive patients. The effect of migration ban strategy was also studied. Four biologically meaningful equilibrium points were found. Their local stability analysis was also carried out. Numerical simulations were carried out, and the most effective strategy to curtail the spread of the disease was shown.

scholarly journals A Mathematical Modeling of Tuberculosis Dynamics with Hygiene Consciousness as a Control Strategy

2020 ◽  
pp. 38-48
Author(s):  
Phineas Z. Mawira ◽  
David M. Malonza
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Control Strategy ◽  
Local Stability ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Linear Ordinary Differential Equations ◽  
Global Stability Analysis ◽  
Local Stability Analysis ◽  
Disease Free

Tuberculosis, an airborne infectious disease, remains a major threat to public health in Kenya. In this study, we derived a system of non-linear ordinary differential equations from the SLICR mathematical model of TB to study the effects of hygiene consciousness as a control strategy against TB in Kenya. The effective basic reproduction number (R0) of the model was determined by the next generation matrix approach. We established and analyzed the equilibrium points. Using the Routh-Hurwitz criterion for local stability analysis and comparison theorem for global stability analysis, the disease-free equilibrium (DFE) was found to be locally asymptotically stable given that R0 < 1.  Also by using the Routh-Hurwitz criterion for local stability analysis and Lyapunov function and LaSalle’s invariance principle for global stability analysis, the endemic equilibrium (EE) point was found to be locally asymptotically stable given that R0 > 1. Using MATLAB ode45 solver, we simulated the model numerically and the results suggest that hygiene consciousness can helpin controlling TB disease if incorporated effectively.

scholarly journals Stability Analysis of Competing Insect Species for a Single Resource

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Sizah Mwalusepo ◽  
Henri E. Z. Tonnang ◽  
Estomih S. Massawe ◽  
Tino Johansson ◽  
Bruno Pierre Le Ru
Keyword(s):  
Stability Analysis ◽  
Local Stability ◽  
Equilibrium Points ◽  
Single Species ◽  
Insect Species ◽  
System Of Differential Equations ◽  
Competing Species ◽  
Local Study ◽  
Interior Equilibrium ◽  
Local Stability Analysis

The models explore the effects of resource and temperature on competition between insect species. A system of differential equations is proposed and analysed qualitatively using stability theory. A local study of the models is performed around axial, planar, and interior equilibrium points to successively estimate the effect of (i) one species interacting with a resource, (ii) two competing species for a single resource, and (iii) three competing species for a single resource. The local stability analysis of the equilibrium is discussed using Routh-Hurwitz criteria. Numerical simulation of the models is performed to investigate the sensitivity of certain key parameters. The models are used to predict population dynamics in the selected cases studied. The results show that when a single species interacts with a resource, the species will be able to establish and sustain a stable population. However, in competing situation, it is observed that the combinations of three parameters (half-saturation, growth rate, and mortality rate) determine which species wins for any given resource. Moreover, our results indicate that each species is the superior competitor for the resource for the range of temperature for which it has the lowest equilibrium resource.

scholarly journals Cournot Duopoly Games: Models and Investigations

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1079 ◽  
Author(s):  
S. S. Askar ◽  
A. Al-khedhairi
Keyword(s):  
Fixed Point ◽  
Bounded Rationality ◽  
Local Stability ◽  
Adjustment Process ◽  
Limited Information ◽  
Cournot Duopoly ◽  
Dynamic Adjustment ◽  
Local Stability Analysis ◽  
Tit For Tat ◽  
Adjustment Parameter

This paper analyzes Cournot duopoly games that are constructed based on Cobb–Douglas preferences. We introduce here two models whose dynamic adjustments depend on bounded rationality, dynamic adjustment, and tit-for-tat mechanism. In the first model, we have two firms with limited information and due to that they adopt the bounded rationality mechanism. They update their productions based on the changing occurred in the marginal profit. For this model, its fixed point is obtained and its stability condition is calculated. In addition, we provide conditions by which this fixed point loses its stability due to flip and Neimark–Sacker bifurcations. Furthermore, numerical simulation shows that this model possesses some chaotic behaviors which are recovered due to corridor stability. In the second model, we handle two different mechanisms of cooperation. These mechanisms are dynamic adjustment process and tit-for-tat strategy. The players who use the dynamic adjustment increase their productions based on the cooperative output while, in tit-for-tat mechanism, they increase the productions based on the cooperative profit. The local stability analysis shows that adopting tit-for-tat makes the model unstable and then the system becomes chaotic for any values of the system’s parameters. The obtained results show that the dynamic adjustment makes the system’s fixed point stable for a certain interval of the adjustment parameter.

scholarly journals Stability behaviour of mathematical model MERS corona virus spread in population

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3947-3960 ◽  
Author(s):  
Muhammad Tahir ◽  
Syed Shah ◽  
Gul Zaman ◽  
Tahir Khan
Keyword(s):  
Stability Analysis ◽  
Local Stability ◽  
Equilibrium Points ◽  
Reproductive Number ◽  
Virus Spread ◽  
Global Stability Analysis ◽  
Local Stability Analysis ◽  
Proposed Model ◽  
Disease Free ◽  
Model Existence

In this subsection, we first formulated the proposed model in there infectious classes and then we derived the basic key value reproductive number, R0 with the help of next generation approach. Then we obtained all the endemic equilibrium points, as well as, local stability analysis, at disease free equilibria and, at endemic equilibria of the related model and shown stable. Further the global stability analysis either, at disease free equilibria, and at endemic equilibria is discussed by constructing Lyapunov function which show the validity of the concern model exist. In the last part of the article numerical simulation is presented for the model which support the model existence with the help of RK-4 method.

Dynamic Analysis of Mechanical Systems With Time-Varying Topologies: Part 1 — Dynamic Model and Stability Analysis

1990 ◽  
Author(s):  
Yu Wang
Keyword(s):  
Stability Analysis ◽  
Dynamic Model ◽  
Local Stability ◽  
Global Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Time Varying ◽  
Discrete Equations ◽  
Local Stability Analysis ◽  
Multiple Collisions

Abstract A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of Poincaré map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of dynamic model and a local stability analysis are presented in Part 1, and the global analysis and numerical simulation are discussed in Part 2.

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