About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 956359, 13 pages
http://dx.doi.org/10.1155/2012/956359
Research Article

An Algebraic Criterion of Zero Solutions of Some Dynamic Systems

1Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China
2Department of Mathematics, Northeast Forestry University, Harbin, Heilongjiang 150040, China

Received 19 October 2012; Revised 7 December 2012; Accepted 7 December 2012

Academic Editor: Allan Peterson

Copyright © 2012 Ying Wang 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. R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York, NY, USA, 1963. View at Zentralblatt MATH
  2. F. G. Boese, “Stability criteria for second-order dynamical systems involving several time delays,” SIAM Journal on Mathematical Analysis, vol. 26, no. 5, pp. 1306–1330, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, NY, USA, 1993.
  4. S. Ruan and J. Wei, “On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion,” IMA Journal of Mathematics Applied in Medicine and Biology, vol. 18, pp. 41–52, 2001.
  5. S. Ruan and J. Wei, “On the zeros of transcendental functions with applications to stability of delay differential equations with two delays,” Dynamics of Continuous, Discrete & Impulsive Systems A, vol. 10, no. 6, pp. 863–874, 2003. View at Zentralblatt MATH
  6. X. Li and J. Wei, “On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays,” Chaos, Solitons and Fractals, vol. 26, no. 2, pp. 519–526, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. C. Huang, Y. He, L. Huang, and Y. Zhaohui, “Hopf bifurcation analysis of two neurons with three delays,” Nonlinear Analysis: Real World Applications, vol. 8, no. 3, pp. 903–921, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. T. Zhang, H. Jiang, and Z. Teng, “On the distribution of the roots of a fifth degree exponential polynomial with application to a delayed neural network model,” Neurocomputing, vol. 72, pp. 1098–1104, 2009.
  9. E. I. Jury, Inners and Stability of Dynamic Systems, John Wiley & Sons, 1974.
  10. B. Zheng, L. Liang, and C. Zhang, “Extended Jury criterion,” Science China Mathematics, vol. 53, no. 4, pp. 1133–1150, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. C. Zhang and B. Zheng, “Stability and bifurcation of a two-dimensional discrete neural network model with multi-delays,” Chaos, Solitons and Fractals, vol. 31, no. 5, pp. 1232–1242, 2007. View at Publisher · View at Google Scholar