Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2010, Article ID 432821, 17 pages
http://dx.doi.org/10.1155/2010/432821
Research Article

Global Hopf Bifurcation Analysis for a Time-Delayed Model of Asset Prices

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 7 October 2009; Accepted 13 January 2010

Academic Editor: Xuezhong He

Copyright © 2010 Ying Qu and Junjie Wei. 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. C. Chiarella, R. Dieci, and L. Gardini, “Speculative behaviour and complex asset price dynamics: a global analysis,” Journal of Economic Behavior and Organization, vol. 49, no. 2, pp. 173–197, 2002. View at Publisher · View at Google Scholar · View at Scopus
  2. C. Chiarella, R. Dieci, and X. He, “Heterogeneity, market mechanisms and asset price dynamics,” in Handbook of Financial Markets: Dynamics and Evolution, chapter 5, pp. 277–344, 2009. View at Google Scholar
  3. C. Chiarella and X.-Z. He, “Heterogeneous beliefs, risk, and learning in a simple asset-pricing model with a market maker,” Macroeconomic Dynamics, vol. 7, no. 4, pp. 503–536, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. G. Dibeh, “Speculative dynamics in a time-delay model of asset prices,” Physica A, vol. 355, no. 1, pp. 199–208, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  5. X.-Z. He, K. Li, J. Wei, and M. Zheng, “Market stability switches in a continuous-time financial market with heterogeneous beliefs,” Economic Modelling, vol. 26, no. 6, pp. 1432–1442, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. C. H. Hommes, “Financial markets as nonlinear adaptive evolutionary systems,” Quantitative Finance, vol. 1, no. 1, pp. 149–167, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  7. C. Hommes, “heterogeneous agent models in economics and finance,” in Handbook of Computational Economics, vol. 2, chapter 23, pp. 1109–1186, 2006. View at Publisher · View at Google Scholar
  8. T. Lux, “The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions,” Journal of Economic Behavior and Organization, vol. 33, no. 2, pp. 143–165, 1998. View at Publisher · View at Google Scholar · View at Scopus
  9. R. Sethi, “Endogenous regime switching in speculative markets,” Structural Change and Economic Dynamics, vol. 7, no. 1, pp. 99–118, 1996. View at Publisher · View at Google Scholar · View at Scopus
  10. J. K. Hale and S. M. V. Lunel, Introduction to Functional-Differential Equations, vol. 99 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1993. View at MathSciNet
  11. J. Carr, Applications of Centre Manifold Theory, vol. 35 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1981. View at Zentralblatt MATH · View at MathSciNet
  12. B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation, vol. 41 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, UK, 1981. View at MathSciNet
  13. J. H. Wu, “Global continua of periodic solutions to some difference-differential equations of neutral type,” The Tohoku Mathematical Journal, vol. 45, no. 1, pp. 67–88, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. Wei, “Bifurcation analysis in a scalar delay differential equation,” Nonlinearity, vol. 20, no. 11, pp. 2483–2498, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. J. Wei and D. Fan, “Hopf bifurcation analysis in a Mackey-Glass system,” International Journal of Bifurcation and Chaos, vol. 17, no. 6, pp. 2149–2157, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. J. Wei and M. Y. Li, “Hopf bifurcation analysis in a delayed Nicholson blowflies equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 60, no. 7, pp. 1351–1367, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J. Wei and C. Yu, “Hopf bifurcation analysis in a model of oscillatory gene expression with delay,” Proceedings of the Royal Society of Edinburgh: Section A, vol. 139, no. 4, pp. 879–895, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  18. J. H. Wu, “Symmetric functional-differential equations and neural networks with memory,” Transactions of the American Mathematical Society, vol. 350, no. 12, pp. 4799–4838, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Y. Li and J. S. Muldowney, “On Bendixson's criterion,” Journal of Differential Equations, vol. 106, no. 1, pp. 27–39, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. K. Engelborghs, T. Luzyanina, and D. Roose, “Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL,” Association for Computing Machinery, vol. 28, no. 1, pp. 1–21, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. K. Engelborghs, T. Luzyanina, and G. Samaey, “DDE-BIFTOOL v. 2.00: a matlab package for bifurcation analysis of delay differential equations,” Technical Report TW-330, Department of Computer Science, K. U. Leuven, Leuven, Belgium, 2001. View at Google Scholar
  22. W. A. Coppel, Stability and Asymptotic Behavior of Differential Equations, D. C. Heath, Boston, Mass, USA, 1965. View at MathSciNet