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Abstract and Applied Analysis
Volume 2013, Article ID 747868, 18 pages
Research Article

Describing the Dynamics and Complexity of Matsumoto-Nonaka's Duopoly Model

Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, C/Doctor Fleming sn, 30202 Cartagena, Spain

Received 12 June 2013; Accepted 8 July 2013

Academic Editor: Luca Guerrini

Copyright © 2013 Jose S. Cánovas and María Muñoz Guillermo. 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.


We study the duopoly model proposed by Matsumoto and Nonaka (2006), in which two firms produce two complementary goods, and there are externalities of different signs. We analyze the topological complexity of the model by computing its topological entropy with prescribed accuracy, and, in addition, we show when such topological complexity is physically observable by characterizing the attractors. Finally, we exploit the fact that reaction maps have negative Schwarzian derivative to show the existence of absolutely continuous (with respect to Lebesgue measure) ergodic measures, and, as an economic application, we compute the average profit for almost all initial conditions.