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Journal of Applied Mathematics
Volume 2014, Article ID 852025, 10 pages
http://dx.doi.org/10.1155/2014/852025
Research Article

Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive Delays

Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200030, China

Received 9 November 2013; Accepted 4 April 2014; Published 4 May 2014

Academic Editor: Mehmet Sezer

Copyright © 2014 Xuhui Li. 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. G. Stépán, “Great delay in a predator-prey model,” Nonlinear Analysis: Theory, Methods & Applications, vol. 10, no. 9, pp. 913–929, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. K. Wang and Y. Zhu, “Global attractivity of positive periodic solution for a Volterra model,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 493–501, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Y. Lv and Z. Du, “Existence and global attractivity of a positive periodic solution to a Lotka-Volterra model with mutual interference and Holling III type functional response,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3654–3664, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. X. Wang, Z. Du, and J. Liang, “Existence and global attractivity of positive periodic solution to a Lotka-Volterra model,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 4054–4061, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. F. Chen, “The permanence and global attractivity of Lotka-Volterra competition system with feedback controls,” Nonlinear Analysis: Real World Applications, vol. 7, no. 1, pp. 133–143, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Y. Song, M. Han, and Y. Peng, “Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays,” Chaos, Solitons & Fractals, vol. 22, no. 5, pp. 1139–1148, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Z. Teng, “On the persistence and positive periodic solution for planar competing Lotka-Volterra systems,” Annals of Differential Equations. Weifen Fangcheng Niankan, vol. 13, no. 3, pp. 275–286, 1997. View at Google Scholar · View at MathSciNet
  8. J. A. Brander and M. S. Taylor, “The simple economics of easter Island: a Ricardo-Malthus model of renewable resource use,” American Economic Review, vol. 88, no. 1, pp. 119–138, 1998. View at Google Scholar · View at Scopus
  9. D. Delfino and P. J. Simmons, “Infectious disease and economic growth: the case of tuberculosis,” Working Paper, 1999. View at Google Scholar
  10. J. D. Farmer, “A simple model for the non equilibrium dynamics and evolution of financial market,” International Journal of Theoretical and Applied Finance, vol. 3, no. 3, pp. 425–441, 2000. View at Publisher · View at Google Scholar
  11. D. M. Kong, “Evolution of market structure under Lotka-Volterra system,” Journal of Industrial Engineering and Engineering Management, vol. 19, no. 3, pp. 77–81, 2005 (Chinese). View at Google Scholar
  12. B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation, Cambridge University Press, Cambridge, UK, 1981.
  13. M. Liao, X. Tang, and C. Xu, “Bifurcation analysis for a three-species predator-prey system with two delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 183–194, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet