scholarly journals Complex Dynamics of a Model with R&D Competition

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2262
Author(s):  
Massimiliano Ferrara ◽  
Tiziana Ciano ◽  
Mariangela Gangemi ◽  
Luca Guerrini
Keyword(s):  
Nash Equilibrium ◽  
Local Stability ◽  
Complex Dynamics ◽  
Two Stage ◽  
Dynamic Behaviors ◽  
Symmetric Structure

The paper analyzes a two-stage oligopoly game of semi-collusion in production described by a system with a symmetric structure. We examine the local stability of a Nash equilibrium and the presence of bifurcations. We discover that the model is capable of exhibiting extremely complicated dynamic behaviors.

scholarly journals Complexity of a Duopoly Game in the Electricity Market with Delayed Bounded Rationality

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Junhai Ma ◽  
Hongliang Tu
Keyword(s):  
Nash Equilibrium ◽  
Bounded Rationality ◽  
Electricity Market ◽  
Complex Dynamics ◽  
Fractal Dimensions ◽  
Practical Significance ◽  
Stable Region ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Game Model

According to a triopoly game model in the electricity market with bounded rational players, a new Cournot duopoly game model with delayed bounded rationality is established. The model is closer to the reality of the electricity market and worth spreading in oligopoly. By using the theory of bifurcations of dynamical systems, local stable region of Nash equilibrium point is obtained. Its complex dynamics is demonstrated by means of the largest Lyapunov exponent, bifurcation diagrams, phase portraits, and fractal dimensions. Since the output adjustment speed parameters are varied, the stability of Nash equilibrium gives rise to complex dynamics such as cycles of higher order and chaos. Furthermore, by using the straight-line stabilization method, the chaos can be eliminated. This paper has an important theoretical and practical significance to the electricity market under the background of developing new energy.

scholarly journals Dynamic Cournot Duopoly Game with Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. A. Elsadany ◽  
A. E. Matouk
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Local Stability ◽  
Stability Region ◽  
Equilibrium Points ◽  
Cournot Duopoly ◽  
Nash Equilibrium Point ◽  
Dynamical Behaviors ◽  
Delayed System

The delay Cournot duopoly game is studied. Dynamical behaviors of the game are studied. Equilibrium points and their stability are studied. The results show that the delayed system has the same Nash equilibrium point and the delay can increase the local stability region.

Complex dynamics analysis for a two-stage Cournot duopoly game of semi-collusion in production

2017 ◽  
Vol 91 (2) ◽  
pp. 819-835 ◽  
Author(s):  
Ya-hui Zhang ◽  
Wei Zhou ◽  
Tong Chu ◽  
Yan-dong Chu ◽  
Jian-ning Yu
Keyword(s):  
Complex Dynamics ◽  
Dynamics Analysis ◽  
Cournot Duopoly ◽  
Two Stage

Imitation Dynamic and Nash Equilibrium in Cournot Oligopoly with Capacities

2003 ◽  
Vol 05 (03) ◽  
pp. 291-305 ◽  
Author(s):  
Alex Possajennikov
Keyword(s):  
Nash Equilibrium ◽  
Imitative Behavior ◽  
Cournot Oligopoly ◽  
Stage Model ◽  
Two Stage

The paper considers an imitation dynamic in the context of Cournot oligopoly. The pure "imitate-the-best" behavior can lead to an outcome inconsistent with Cournot-Nash equilibrium. The paper extends purely imitative behavior to imperfect imitation in the two-stage model with capacities and prices. This variation in the imitative behavior improves efficiency and makes the Cournot-Nash equilibrium a possible outcome of the dynamic imitation process.

scholarly journals Backward and Hopf bifurcation analysis of an SEIRS COVID-19 epidemic model with saturated incidence and saturated treatment response

2020 ◽  
Author(s):  
David A. Oluyori ◽  
Ángel G. C. Pérez ◽  
Victor A. Okhuese ◽  
Muhammad Akram
Keyword(s):  
Hopf Bifurcation ◽  
Local Stability ◽  
Complex Dynamics ◽  
Reproduction Number ◽  
Backward Bifurcation ◽  
Treatment Measures ◽  
Saturated Incidence ◽  
Second Wave ◽  
Saturated Treatment ◽  
Disease Free

AbstractIn this work, we further the investigation of an SEIRS model to study the dynamics of the Coronavirus Disease 2019 pandemic. We derive the basic reproduction number R0 and study the local stability of the disease-free and endemic states. Since the condition R0 < 1 for our model does not determine if the disease will die out, we consider the backward bifurcation and Hopf bifurcation to understand the dynamics of the disease at the occurrence of a second wave and the kind of treatment measures needed to curtail it. Our results show that the limited availability of medical resources favours the emergence of complex dynamics that complicates the control of the outbreak.

scholarly journals Complex Dynamics in Nonlinear Triopoly Market with Different Expectations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Junhai Ma ◽  
Xiaosong Pu
Keyword(s):  
Local Stability ◽  
Demand Function ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Game Model ◽  
Bifurcation Diagrams ◽  
Nonlinear Difference Equations ◽  
Total Cost ◽  
Attractor Bifurcation ◽  
Total Cost Function

A dynamic triopoly game characterized by firms with different expectations is modeled by three-dimensional nonlinear difference equations, where the market has quadratic inverse demand function and the firm possesses cubic total cost function. The local stability of Nash equilibrium is studied. Numerical simulations are presented to show that the triopoly game model behaves chaotically with the variation of the parameters. We obtain the fractal dimension of the strange attractor, bifurcation diagrams, and Lyapunov exponents of the system.

COMPLEX DYNAMICS AND CHAOS CONTROL IN NONLINEAR FOUR-OLIGOPOLIST GAME WITH DIFFERENT EXPECTATIONS

2013 ◽  
Vol 23 (03) ◽  
pp. 1350053 ◽  
Author(s):  
XIAOSONG PU ◽  
JUNHAI MA
Keyword(s):  
Local Stability ◽  
Chaos Control ◽  
Demand Function ◽  
Complex Dynamics ◽  
Parameter Variation ◽  
Variation Method ◽  
State Variables ◽  
Total Cost ◽  
Proposed Model ◽  
Total Cost Function

A dynamic four-oligopolist game characterized by firms with different expectations is modeled by four-dimensional nonlinear difference equations, where the market has a quadratic inverse demand function and the firm possesses a cubic total cost function. The Nash equilibrium of the local stability of the proposed model is studied. Then the bifurcation diagrams and Lyapunov exponents of the system are presented to show that four-oligopolist game model behaves chaotically with the variation of the parameters. Finally, the state variables' feedback and parameter variation method are effectively used to control the delay in the appearance of bifurcation.

scholarly journals Complex Dynamics in a Mixed Duopoly Game Based on Relative Profit Maximization

2021 ◽  
pp. 47-57
Author(s):  
Yuqi Dou ◽  
Xingyu Liu
Keyword(s):  
Nash Equilibrium ◽  
Dynamic Systems ◽  
Complex Dynamics ◽  
Rational Expectation ◽  
Profit Maximization ◽  
Mixed Duopoly ◽  
Complex Dynamic ◽  
Discrete Dynamic Systems ◽  
The Stability ◽  
Relative Profit

In this paper, the complex dynamic behavior of a mixed duopoly game model is studied. Based on the principle of relative profit maximization and bounded rational expectation, the corresponding discrete dynamic systems are constructed in the case of nonlinear cost function. In theory, the conditions for the local stability of Nash equilibrium are given. In terms of numerical experiments, bifurcation diagrams are used to depict the effects of product differences, adjustment speed, and other parameters on the stability of Nash equilibrium.

Flow Dynamic Behaviors and Characteristics of Two-Stage Viscous Pump in Microchannels

2008 ◽  
Author(s):  
Jianfeng Lu ◽  
Jing Ding
Keyword(s):  
Reynolds Number ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Small Distance ◽  
Flow Dynamic ◽  
Two Stage ◽  
Dynamic Behaviors ◽  
Viscous Pump ◽  
Identical Type

The flow dynamic behaviors and characteristics of a two-stage viscous pump with two rotating cylinderes in microchannels were numerically studied by laminar model. At low Reynolds numbers, the dimensionless mass flow rate almost keeps constant for similar flow structure in the identical type of pump, and it also has little variation with different types of pump expect for the staggered pump with very small distance between different cylinders. As the Reynolds number increasing, the dimensionless mass flow rate drops because of the vortices evolution, and the distance between different cylinders significantly affects the flow dynamic process. For large distance, two steady vortices appear behind the cylinders, and the flow dynamics of aligned and staggered pump are very similar. For small distance, the flow rate of the staggered pump almost decreases with the distance rising, while the flow rate of the aligned pump has a maximum at a specific distance. Corresponding to the single-stage pump, the mass flow rate of two-stage pump is remarkably enhanced, and the enhanment ratio will increase as Reynolds number droping. Meanwhile, the driving power of two cylinders drops very slowly as the distance decreasing.

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