Abstract and Applied Analysis

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

Junhai Ma, Fang Zhang, and Yanyan He

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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.

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Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 970205, 13 pages.

First available in Project Euclid: 27 February 2015

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Ma, Junhai; Zhang, Fang; He, Yanyan. Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 970205, 13 pages. doi:10.1155/2014/970205. https://projecteuclid.org/euclid.aaa/1425048776

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