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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 970205, 13 pages
http://dx.doi.org/10.1155/2014/970205
Research Article

Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control

1College of Management and Economics, Tianjin University, Tianjin 300072, China
2Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

Received 11 April 2014; Revised 11 June 2014; Accepted 18 June 2014; Published 13 August 2014

Academic Editor: Simone Marsiglio

Copyright © 2014 Junhai Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.