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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 747868, 18 pages
http://dx.doi.org/10.1155/2013/747868
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.

Linked References

  1. A. Matsumoto and N. Nonaka, “Statistical dynamics in a chaotic Cournot model with complementary goods,” Journal of Economic Behavior & Organization, vol. 61, pp. 769–783, 2006. View at Publisher · View at Google Scholar
  2. A. Agliari and F. Bignami, “Multistability and global dynamics in a complementary good market model,” Pure Mathematics and Applications, vol. 16, no. 4, pp. 319–343, 2005. View at MathSciNet
  3. R. L. Adler, A. G. Konheim, and M. H. McAndrew, “Topological entropy,” Transactions of the American Mathematical Society, vol. 114, pp. 309–319, 1965. View at Publisher · View at Google Scholar · View at MathSciNet
  4. M. Misiurewicz and W. Szlenk, “Entropy of piecewise monotone mappings,” Studia Mathematica, vol. 67, no. 1, pp. 45–63, 1980. View at MathSciNet
  5. R.-A. Dana and L. Montrucchio, “Dynamic complexity in duopoly games,” Journal of Economic Theory, vol. 40, no. 1, pp. 40–56, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  6. L. Block, J. Keesling, S. H. Li, and K. Peterson, “An improved algorithm for computing topological entropy,” Journal of Statistical Physics, vol. 55, no. 5-6, pp. 929–939, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  7. P. Collet, J. P. Crutchfield, and J.-P. Eckmann, “Computing the topological entropy of maps,” Communications in Mathematical Physics, vol. 88, no. 2, pp. 257–262, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  8. L. Block and J. Keesling, “Computing the topological entropy of maps of the interval with three monotone pieces,” Journal of Statistical Physics, vol. 66, no. 3-4, pp. 755–774, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. S. Cánovas and M. M. Guillermo, “Computing topological entropy for periodic sequences of unimodal maps,” preprint.
  10. F. Blanchard, E. Glasner, S. Kolyada, and A. Maass, “On Li-Yorke pairs,” Journal für die Reine und Angewandte Mathematik, vol. 547, pp. 51–68, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  11. M. Martens, W. de Melo, and S. van Strien, “Julia-Fatou-Sullivan theory for real one-dimensional dynamics,” Acta Mathematica, vol. 168, no. 1, pp. 273–318, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  12. F. Balibrea and V. J. López, “The measure of scrambled sets: a survey,” Acta Universitatis Matthiae Belii, no. 7, pp. 3–11, 1999. View at MathSciNet
  13. J. Smítal, “Chaotic functions with zero topological entropy,” Transactions of the American Mathematical Society, vol. 297, no. 1, pp. 269–282, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  14. W. de Melo and S. van Strien, One-Dimensional Dynamics, vol. 25 of Modern Surveys in Mathematics, Springer, New York, NY, USA, 1993. View at MathSciNet
  15. J. Guckenheimer, “Sensitive dependence to initial conditions for one-dimensional maps,” Communications in Mathematical Physics, vol. 70, no. 2, pp. 133–160, 1979. View at Publisher · View at Google Scholar · View at MathSciNet
  16. P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, vol. 1 of Progress in Physics, Birkhäuser, Boston, Mass, USA, 1980. View at MathSciNet
  17. D. Singer, “Stable orbits and bifurcation of maps of the interval,” SIAM Journal on Applied Mathematics, vol. 35, no. 2, pp. 260–267, 1978. View at Publisher · View at Google Scholar · View at MathSciNet
  18. F. Balibrea, A. Linero, and J. S. Cánovas, “On ω-limit sets of antitriangular maps,” Topology and its Applications, vol. 137, no. 1–3, pp. 13–19, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  19. F. Balibrea, A. Linero, and J. S. Canovas, “Minimal sets of antitriangular maps,” International Journal of Bifurcation and Chaos, vol. 13, no. 7, pp. 1733–1741, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  20. P. Walters, An Introduction to Ergodic Theory, vol. 79 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1982. View at MathSciNet
  21. S. D. Johnson, “Singular measures without restrictive intervals,” Communications in Mathematical Physics, vol. 110, no. 2, pp. 185–190, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  22. F. Balibrea, V. J. López, and J. S. C. Peña, “Some results on entropy and sequence entropy,” International Journal of Bifurcation and Chaos, vol. 9, no. 9, pp. 1731–1742, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  23. H. Bruin, W. Shen, and S. van Strien, “Existence of unique SRB-measures is typical for real unicritical polynomial families,” Annales Scientifiques de l'École Normale Supérieure, vol. 39, no. 3, pp. 381–414, 2006. View at Publisher · View at Google Scholar · View at MathSciNet