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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 929186, 6 pages
http://dx.doi.org/10.1155/2013/929186
Research Article

Stability Switches in a First-Order Complex Neutral Delay Equation

Departamento de Matemática Aplicada, Universidad de Alicante, Apartado Postal 99, 03080 Alicante, Spain

Received 23 July 2012; Accepted 12 November 2012

Academic Editor: Samir H. Saker

Copyright © 2013 M. Roales and F. Rodríguez. 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. K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer, Dordrecht, The Netherlands, 1992. View at Zentralblatt MATH
  2. R. D. Driver, “A mixed neutral system,” Nonlinear Analysis: Theory, Methods and Applications A, vol. 8, no. 2, pp. 155–158, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. R. K. Brayton and R. A. Willoughby, “On the numerical integration of a symmetric system of difference-differential equations of neutral type,” Journal of Mathematical Analysis and Applications, vol. 18, pp. 182–189, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. B. Cahlon and D. Schmidt, “On stability of a first-order complex delay differential equation,” Nonlinear Analysis: Real World Applications, vol. 3, no. 3, pp. 413–429, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. J. Wei and C. Zhang, “Stability analysis in a first-order complex differential equations with delay,” Nonlinear Analysis: Theory, Methods and Applications A, vol. 59, no. 5, pp. 657–671, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. K. L. Cooke and Z. Grossman, “Discrete delay, distributed delay and stability switches,” Journal of Mathematical Analysis and Applications, vol. 86, no. 2, pp. 592–627, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. E. Beretta and Y. Kuang, “Geometric stability switch criteria in delay differential systems with delay dependent parameters,” SIAM Journal on Mathematical Analysis, vol. 33, no. 5, pp. 1144–1165, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Arizona, Ariz, USA, 1993.
  9. 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. View at Google Scholar
  10. 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
  11. J. Li, L. Zhang, and Z. Wang, “Two effective stability criteria for linear time-delay systems with complex coefficients,” Journal of Systems Science and Complexity, vol. 24, no. 5, pp. 835–849, 2011. View at Publisher · View at Google Scholar
  12. M. S. Lee and C. S. Hsu, “On the τ-decomposition method of stability analysis for retarded dynamical systems,” SIAM Journal on Control and Optimization, vol. 7, pp. 215–233, 1969. View at Google Scholar
  13. K. L. Cooke and P. van den Driessche, “On zeroes of some transcendental equations,” Funkcialaj Ekvacioj, vol. 29, no. 1, pp. 77–90, 1986. View at Google Scholar · View at Zentralblatt MATH