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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.

Linked References

  1. H. N. Agiza, “On the analysis of stability, bifurcation, chaos and chaos control of Kopel map,” Chaos, Solitons & Fractals, vol. 10, no. 11, pp. 1909–1916, 1999. View at Publisher · View at Google Scholar · View at Scopus
  2. G. I. Bischi and A. Naimzada, “Global analysis of a dynamic duopoly game with bounded rationality,” in Advances in Dynamic Games and Application, vol. 5, pp. 361–385, Birkhäuser, Basel, Switzerland, 2000. View at MathSciNet
  3. H. N. Agiza, A. S. Hegazi, and A. A. Elsadany, “Complex dynamics and synchronization of a duopoly game with bounded rationality,” Mathematics and Computers in Simulation, vol. 58, no. 2, pp. 133–146, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. F. Tramontana, “Heterogeneous duopoly with isoelastic demand function,” Economic Modelling, vol. 27, no. 1, pp. 350–357, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. Y. Fan, T. Xie, and J. Du, “Complex dynamics of duopoly game with heterogeneous players: a further analysis of the output model,” Applied Mathematics and Computation, vol. 218, no. 15, pp. 7829–7838, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. L. Fanti and L. Gori, “The dynamics of a differentiated duopoly with quantity competition,” Economic Modelling, vol. 29, no. 2, pp. 421–427, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. T. Puu, “Complex dynamics with three oligopolists,” Chaos, Solitons and Fractals, vol. 7, no. 12, pp. 2075–2081, 1996. View at Publisher · View at Google Scholar · View at Scopus
  8. H. N. Agiza and A. A. Elsadany, “Chaotic dynamics in nonlinear duopoly game with heterogeneous players,” Applied Mathematics and Computation, vol. 149, no. 3, pp. 843–860, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. J. Zhang and J. Ma, “Research on the price game model for four oligarchs with different decision rules and its chaos control,” Nonlinear Dynamics, vol. 70, no. 1, pp. 323–334, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. A. K. Naimzada and F. Tramontana, “Dynamic properties of a Cournot-Bertrand duopoly game with differentiated products,” Economic Modelling, vol. 29, no. 4, pp. 1436–1439, 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. C. H. Tremblay and V. J. Tremblay, “The Cournot-Bertrand model and the degree of product differentiation,” Economics Letters, vol. 111, no. 3, pp. 233–235, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. J. Ma and X. Pu, “The research on Cournot-Bertrand duopoly model with heterogeneous goods and its complex characteristics,” Nonlinear Dynamics, vol. 72, no. 4, pp. 895–903, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. B. Xin and T. Chen, “On a master-slave Bertrand game model,” Economic Modelling, vol. 28, no. 4, pp. 1864–1870, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. M. T. Yassen and H. N. Agiza, “Analysis of a duopoly game with delayed bounded rationality,” Applied Mathematics and Computation, vol. 138, no. 2-3, pp. 387–402, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. J. Peng, Z. Miao, and F. Peng, “Study on a 3-dimensional game model with delayed bounded rationality,” Applied Mathematics and Computation, vol. 218, no. 5, pp. 1568–1576, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. J. Ma and K. Wu, “Complex system and influence of delayed decision on the stability of a triopoly price game model,” Nonlinear Dynamics, vol. 73, no. 3, pp. 1741–1751, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. T. Dubiel-Teleszynski, “Nonlinear dynamics in a heterogeneous duopoly game with adjusting players and diseconomies of scale,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 1, pp. 296–308, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. B. Xin, T. Chen, and J. Ma, “Neimark-Sacker bifurcation in a discrete-time financial system,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 405639, 12 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. A. A. Elsadany, “Competition analysis of a triopoly game with bounded rationality,” Chaos, Solitons and Fractals, vol. 45, no. 11, pp. 1343–1348, 2012. View at Publisher · View at Google Scholar · View at Scopus
  20. S. Elaydi, An Introduction to Difference Equations, Springer, New York, NY, USA, 2005. View at MathSciNet
  21. K. Pyragas, “Continuous control of chaos by self-controlling feedback,” Physics Letters A, vol. 170, no. 6, pp. 421–428, 1992. View at Publisher · View at Google Scholar · View at Scopus
  22. J. A. Holyst and K. Urbanowicz, “Chaos control in economical model by time-delayed feedback method,” Physica A: Statistical Mechanics and its Applications, vol. 287, no. 3-4, pp. 587–598, 2000. View at Publisher · View at Google Scholar · View at Scopus
  23. J. Du, T. Huang, Z. Sheng, and H. Zhang, “A new method to control chaos in an economic system,” Applied Mathematics and Computation, vol. 217, no. 6, pp. 2370–2380, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  24. J. Du, Y. Fan, Z. Sheng, and Y. Hou, “Dynamics analysis and chaos control of a duopoly game with heterogeneous players and output limiter,” Economic Modelling, vol. 33, pp. 507–516, 2013. View at Publisher · View at Google Scholar · View at Scopus