Complexity analysis of a master-slave oligopoly model and chaos control
type: Item
instance of: scholarly article
title: Complexity analysis of a master-slave oligopoly model and chaos control
zbMATH Open document ID: 1406.91245
DOI: 10.1155/2014/970205
author: Junhai Ma
author: Fang Zhang
author: Yanyan He
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We establish a master-slave oligopoly game model with an upstream monopoly whose output is considered and two downstream oligopolies whose prices are considered. The existence and the local stable region of the Nash equilibrium point are investigated. The complex dynamic properties, such as bifurcation and chaos, are analyzed using bifurcation diagrams, the largest Lyapunov exponent diagrams, and the strange attractor graph. We further analyze the long-run average profit of the three firms and find that they are all optimal in the stable region. In addition, delay feedback control method and limiter control method are used in nondelayed model to control chaos. Furthermore, a delayed master-slave oligopoly game model is considered, and the three firms' profit in various conditions is analyzed. We find that suitable delayed parameters are important for eliminating chaos and maximizing the profit of the players.
Mathematics Subject Classification ID: 91B54
Mathematics Subject Classification ID: 91A80
Mathematics Subject Classification ID: 68Q17
Mathematics Subject Classification ID: 34H10
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 7023424
zbMATH Keywords: master-slave oligopoly
zbMATH Keywords: complexity
zbMATH Keywords: chaos control
zbMATH Keywords: bifurcation
zbMATH Keywords: oligopoly game model
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/970205
OpenAlex ID: W2045272717
Wikidata QID: Q59043212
cites work: On the analysis of stability, bifurcation, chaos and chaos control of Kopel map
cites work: Q4504056
cites work: Complex dynamics and synchronization of a duopoly game with bounded rationality
cites work: Complex dynamics of duopoly game with heterogeneous players: a further analysis of the output model
cites work: Chaotic dynamics in nonlinear duopoly game with heterogeneous players.
cites work: The Cournot-Bertrand model and the degree of product differentiation
cites work: Analysis of a duopoly game with delayed bounded rationality.
cites work: Study on a 3-dimensional game model with delayed bounded rationality
cites work: Nonlinear dynamics in a heterogeneous duopoly game with adjusting players and diseconomies of scale
cites work: Neimark-Sacker bifurcation in a discrete-time financial system
cites work: Q4679023
cites work: A new method to control chaos in an economic system
Recommended article: Complex nonlinear dynamics and controlling chaos in a Cournot duopoly economic model
Recommended article: Dynamical analysis and chaos control in a heterogeneous Kopel duopoly game
Recommended article: Chaos control and anticontrol of the output duopoly competing evolution model
Recommended article: Q3307779
Recommended article: Complex dynamics and chaos control in nonlinear four-oligopolist game with different expectations
Recommended article: Nonlinear analysis and chaos control of the complex dynamics of multi-market Cournot game with bounded rationality
Recommended article: Controlling the Cournot-Nash chaos
Recommended article: Complex dynamics and chaos control on a kind of Bertrand duopoly game model considering R\&D activities
Recommended article: Complex dynamics and chaos control of heterogeneous quadropoly game
description: scientific article; zbMATH DE number 7023424