Free Access
Math. Model. Nat. Phenom.
Volume 4, Number 2, 2009
Delay equations in biology
Page(s) 1 - 27
Published online 26 March 2009
  1. M. Adimy, F. Crauste, S. Ruan. A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J. Appl. Math., 65 (2005), 1328–1352. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Adimy, F. Crauste, S. Ruan. Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics. Nonl. Anal.: Real World Appl., 6 (2005), 651–670. [Google Scholar]
  3. J. Arino, P. van den Driessche. Time delays in epidemic models: modeling and numerical considerations, in Delay differential equations and applications, chapter 13, 539–558. Springer, Dordrecht, 2006. [Google Scholar]
  4. F.M. Atay. Distributed delays facilitate amplitude death of coupled oscillators. Phys. Rev. Lett., 91 (2003), 094101. [CrossRef] [PubMed] [Google Scholar]
  5. F.M. Atay. Oscillator death in coupled functional differential equations near Hopf bifurcation. J. Diff. Eqs., 221 (2006), 190–209. [Google Scholar]
  6. F.M. Atay. Delayed feedback control near Hopf bifurcation. DCDS, 1 (2008), 197–205. [Google Scholar]
  7. S. Bernard, J. Bélair, M.C. Mackey. Sufficient conditions for stability of linear differential equations with distributed delay. DCDS, 1B (2001), 233–256. [Google Scholar]
  8. F. Brauer, C. Castillo-Chávez. Mathematical models in population biology and epidemiology. Springer, New York, 2001. [Google Scholar]
  9. S.A. Campbell, I. Ncube. Some effects of gamma distribution on the dynamics of a scalar delay differential equation. Preprint, (2009). [Google Scholar]
  10. Y. Chen. Global stability of neural networks with distributed delays. Neur. Net., 15 (2002), 867–871. [CrossRef] [Google Scholar]
  11. Y. Chen. Global stability of delayed Cohen-Grossberg neural networks. IEEE Trans. Circuits Syst.-I, 53 (2006), 351–357. [CrossRef] [MathSciNet] [Google Scholar]
  12. R.V. Churchill, J.W. Brown. Complex variables and applications. McGraw-Hill, New York, 1984. [Google Scholar]
  13. K.L. Cooke, Z. Grossman. Discrete delay, distributed delay and stability switches. J. Math. Anal. Appl., 86 (1982), 592–627. [CrossRef] [MathSciNet] [Google Scholar]
  14. J.M. Cushing. Integrodifferential equations and delay models in population dynamics, Vol. 20 of Lecture Notes in Biomathematics. Springer-Verlag, Berlin, New York, 1977. [Google Scholar]
  15. T. Faria, J.J. Oliveira. Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks. J. Diff. Eqs., 244 (2008), 1049–1079. [CrossRef] [Google Scholar]
  16. K. Gopalsamy. Stability and oscillations in delay differential equations of population dynamics. Kluwer, Dordrecht, 1992. [Google Scholar]
  17. K. Gopalsamy and X.-Z. He. Stability in asymmetric Hopfield nets with transmission delays. Physica D, 76 (1994), 344–358. [CrossRef] [MathSciNet] [Google Scholar]
  18. R.V. Hogg and A.T. Craig. Introduction to mathematical statistics. Prentice Hall, United States, 1995. [Google Scholar]
  19. G.E. Hutchinson. Circular cause systems in ecology. Ann. N.Y. Acad. Sci., 50 (1948), 221–246. [Google Scholar]
  20. V.K. Jirsa, M. Ding. Will a large complex system with delays be stable?. Phys. Rev. Lett., 93 (2004), 070602. [CrossRef] [PubMed] [Google Scholar]
  21. K. Koch. Biophysics of computation: information processing in single neurons. Oxford University Press, New York, 1999. [Google Scholar]
  22. Y. Kuang. Delay differential equations: with applications in population dynamics, Vol. 191 of Mathematics in Science and Engineering. Academic Press, New York, 1993. [Google Scholar]
  23. X. Liao, K.-W. Wong, Z. Wu. Bifurcation analysis on a two-neuron system with distributed delays. Physica D, 149 (2001), 123–141. [CrossRef] [MathSciNet] [Google Scholar]
  24. N. MacDonald. Time lags in biological models, Vol. 27 of Lecture Notes in Biomathematics. Springer-Verlag, Berlin; New York, 1978. [Google Scholar]
  25. N. MacDonald. Biological delay systems: linear stability theory. Cambridge University Press, Cambridge, 1989. [Google Scholar]
  26. M.C. Mackey, U. an der Heiden. The dynamics of recurrent inhibition. J. Math. Biol., 19 (1984), 211–225. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  27. J.M. Milton. Dynamics of small neural populations, Vol. 7 of CRM monograph series. American Mathematical Society, Providence, 1996. [Google Scholar]
  28. S. Ruan. Delay differential equations for single species dynamics, in Delay differential equations and applications, chapter 11, 477–515. Springer, Dordrecht, 2006. [Google Scholar]
  29. S. Ruan, R.S. Filfil. Dynamics of a two-neuron system with discrete and distributed delays. Physica D, 191 (2004), 323–342. [CrossRef] [MathSciNet] [Google Scholar]
  30. A. Thiel, H. Schwegler, C.W. Eurich. Complex dynamics is abolished in delayed recurrent systems with distributed feedback times. Complexity, 8 (2003), 102–108. [CrossRef] [MathSciNet] [Google Scholar]
  31. G.S.K. Wolkowicz, H. Xia, S. Ruan. Competition in the chemostat: A distributed delay model and its global asymptotic behaviour. SIAM J. Appl. Math., 57 (1997), 1281–1310. [CrossRef] [MathSciNet] [Google Scholar]
  32. G.S.K. Wolkowicz, H. Xia, J. Wu. Global dynamics of a chemostat competition model with distributed delay. J. Math. Biol., 38 (1999), 285–316. [CrossRef] [MathSciNet] [Google Scholar]
  33. P. Yan. Separate roles of the latent and infectious periods in shaping the relation between the basic reproduction number and the intrinsic growth rate of infectious disease outbreaks. J. Theoret. Biol., 251 (2008), 238–252. [CrossRef] [Google Scholar]

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