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March  2010, 13(2): 269-278. doi: 10.3934/dcdsb.2010.13.269

Detecting chaos in a duopoly model via symbolic dynamics

Jose S. Cánovas 1, , Tönu Puu 2, and  Manuel Ruiz Marín 3,

1. 

Dpto. Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Dr. Fleming s/n 30202, Cartagena, Spain
2. 

Centre for Regional Science, Umeå University, SE-90187 Umeå, Sweden
3. 

Dpto. Métodos Cuantitativos e Informáticos, Universidad Politécnica de Cartagena, Paseo Alfonso XIII 50, 30203, Cartagena, Spain

Received  March 2008 Revised  March 2009 Published  December 2009

This paper considers a Cournot duopoly model assuming isoelastic demand and smooth cost functions with built-in capacity limits. When the firms cannot obtain positive profits they are assumed to choose small "stand-by" outputs rather than closing down, in order to avoid substantial fitting up costs when market conditions turn out more favorable. It is shown that the model provides chaotic behavior. In particular, the system has positive topological entropy and hence the map is chaotic in the Li-Yorke sense. Moreover, chaos is not only topological but also physically observable.
Keywords: nonautonomous systems., Li-Yorke chaos, topological entropy, Duopoly games.
Mathematics Subject Classification: Primary: 37N40, 37B55; Secondary: 37B4.
Citation: Jose S. Cánovas, Tönu Puu, Manuel Ruiz Marín. Detecting chaos in a duopoly model via symbolic dynamics. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 269-278. doi: 10.3934/dcdsb.2010.13.269
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