- Z. Agur, L. Cojocaru, R. Anderson and Y. Danon, Pulse mass measles vaccination across age cohorts. Proc. Natl. Acad. Sci. USA 90 (1993) 11698–11702. [CrossRef]
- W.G. Aiello and H.I. Freedman, A time delay model of single-species growth with stage structure. Math. Biosci. 101 (1990) 139–153. [CrossRef] [MathSciNet] [PubMed]
- W.G. Aiello, H.I. Freedman and J. Wu, Analysis of a model representing stage structured population growth with state-dependent time delay. SIAM J. Appl. Math. 52 (1990) 855–869. [CrossRef]
- D.D. Bainov and P.S. Simeonov, System with impulsive effect: stability, theory and applications. John Wiley & Sons, New York (1989).
- J.R. Bence and R.M. Nisbet, Space limited recruitment in open systems: The importance of time delays. Ecology 70 (1989) 1434–1441. [CrossRef]
- O. Bernard and J.L. Gouzé, Transient behavior of biological loop models, with application to the droop model. Math. Biosci. 127 (1995) 19–43. [CrossRef] [MathSciNet] [PubMed]
- O. Bernard and S. Souissi, Qualitative behavior of stage-structure populations: application to structure validation. J. Math. Biol. 37 (1998) 291–308. [CrossRef] [MathSciNet]
- L.W. Botsford, Further analysis of Clark's delayed recruitment model. Bull. Math. Biol. 54 (1992) 275–293.
- J.M. Cushing, Equilibria and oscillations in age-structured population growth models, in Mathematical modelling of environmental and ecological system, J.B. Shukla, T.G. Hallam and V. Capasso Eds., Elsevier, New York (1987) 153–175.
- J.M. Cushing, An introduction to structured population dynamics. CBMS-NSF Regional Conf. Ser. in Appl. Math. 71 (1998) 1–10.
- I.R. Epstein, Oscillations and chaos in chemical systems. Phys. D 7 (1983) 47–56. [CrossRef]
- J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Springer Verlag, Berlin, Heidelberg, New York, Tokyo (1990).
- J. Guckenheimer, G. Oster and A. Ipaktchi, The dynamics of density dependent population models. J. Math. Biol. 4 (1977) 101–147. [MathSciNet]
- W.S.C. Gurney, R.M. Nisbet and J.L. Lawton, The systematic formulation of tractable single-species population models incorporating age-structure. J. Anim. Ecol. 52 (1983) 479–495. [CrossRef]
- W.S.C. Gurney, R.M. Nisbet and S.P. Blythe, The systematic formulation of model of predator prey populations. Springer, J.A.J. Metz and O. Dekmann Eds., Berlin, Heidelberg, New York, Lecture Notes Biomath. 68 (1986).
- A. Hastings, Age-dependent predation is not a simple process. I. continuous time models. Theor. Popul. Biol. 23 (1983) 347–362. [CrossRef]
- S.P. Hastings, J.J. Tyson and D. Webster, Existence of periodic solutions for negative feedback cellular control systems. J. Differential Equations 25 (1977) 39–64. [CrossRef] [MathSciNet]
- M.J.B. Hauser, L.F. Olsen, T.V. Bronnikova and W.M. Schaffer, Routes to chaos in the peroxidase-oxidase reaction: period-doubling and period-adding. J. Phys. Chem. B 101 (1997) 5075–5083. [CrossRef]
- S.M. Henson, Leslie matrix models as “stroboscopic snapshots" of McKendrick PDE models. J. Math. Biol. 37 (1998) 309–328. [CrossRef] [MathSciNet]
- Y.F. Hung, T.C. Yen and J.L. Chern, Observation of period-adding in an optogalvanic circuit. Phys. Lett. A 199 (1995) 70–74. [CrossRef]
- E.I. Jury, Inners and stability of dynamic systems. Wiley, New York (1974).
- K. Kaneko, On the period-adding phenomena at the frequency locking in a one-dimensional mapping. Progr. Theoret. Phys. 69 (1982) 403–414. [CrossRef] [MathSciNet]
- K. Kaneko, Similarity structure and scaling property of the period-adding phenomena. Progr. Theoret. Phys. 69 (1983) 403–414. [CrossRef] [MathSciNet]
- M.J. Kishi, S. Kimura, H. Nakata and Y. Yamashita, A biomass-based model for the sand lance in Seto Znland Sea. Japan. Ecol. Model. 54 (1991) 247–263. [CrossRef]
- A. Lakmeche and O. Arino, Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment. Dynam. Contin. Discrete Impuls. Systems 7 (2000) 165–287.
- V. Laksmikantham, D.D. Bainov and P.S. Simeonov, Theory of impulsive differential equations. World Scientific, Singapore (1989).
- P.H. Leslie, Some further notes on the use of matrices in certain population mathematics. Biometrika 35 (1948) 213–245. [MathSciNet]
- S.A. Levin, Age-structure and stability in multiple-age spawning populations. Springer-Verlag, T.L. Vincent and J.M. Skowrinski Eds., Berlin, Heidelberg, New York, Lecture Notes Biomath. 40 (1981) 21–45.
- S.A. Levin and C.P. Goodyear, Analysis of an age-structured fishery model. J. Math. Biol. 9 (1980) 245–274. [CrossRef] [MathSciNet]
- T. Lindstrom, Dependencies between competition and predation-and their consequences for initial value sensitivity. SIAM J. Appl. Math. 59 (1999) 1468–1486. [CrossRef] [MathSciNet]
- J.A.J. Metz and O. Diekmann, The dynamics of physiologically structured populations. Springer, Berlin, Heidelberg, New York, Lecture notes Biomath. 68 (1986).
- A.J. Nicholson, An outline of the dynamics of animal populations. Aust. J. Zool. 2 (1954) 9–65. [CrossRef]
- A.J. Nicholson, The self adjustment of populations to change. Cold Spring Harbor Symp. Quant. Biol. 22 (1957) 153–173.
- J.C. Panetta, A mathematical model of periodically pulsed chemotherapy: tumor recurrence and metastasis in a competition environment. Bull. Math. Biol. 58 (1996) 425–447. [CrossRef] [PubMed]
- B. Shulgin, L. Stone and Z. Agur, Pulse vaccination strategy in the SIR epidemic model. Bull. Math. Biol. 60 (1998) 1–26. [CrossRef] [PubMed]
- S.Y. Tang and L.S. Chen, Density-dependent birth rate, birth pulses and their population dynamic consequences. J. Math. Biol. 44 (2002) 185–199. [CrossRef] [MathSciNet] [PubMed]
- G. Uribe, On the relationship between continuous and discrete models for size-structured population dynamics. Ph.D. dissertation, Interdisciplinary program in applied mathematics, University of Arizona, Tucson, USA (1993).
Volume 37, Number 3, May-June 2003
|Page(s)||433 - 450|
|Published online||15 April 2004|