A Nonlinear Age and Maturity Structured Model of Population Dynamics: I. Basic Theory

Journal of Mathematical Analysis and Applications

Volumn 242, Issue 1, 2000, Pages 93-104

  Dyson, Janet ^a   Villella Bressan, Rosanna ^b   Webb, Glenn ^c  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF PADOVA   (Italy)

^c VANDERBILT UNIVERSITY   (United States)

Author keywords

Population problems; semigroup of operators; asymptotic behavior

Indexed keywords

EID: 0010023887     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1999.6656     Document Type: Article

References (20)

1. Crabb R., Losson J., Mackey M. C. Propagating fronts, chaos and multi-stability in a cell replication model. Chaos. 3:1996b;477-492.
2. Dyson J., Villella-Bressan R., Webb G. F. A singular transport equation modelling a proliferating maturity structured cell population. Canad. Appl. Math. Quart. 4:1996;65-95.
3. Dyson J., Villella-Bressan R., Webb G. F. A semilinear transport equation with delays. The Proceedings of the 2nd Marrakesh International Conference on Differential Equations. 1996.
4. Dyson J., Villella-Bressan R., Webb G. F. Hypercyclicity of solutions of a transport equation with delays. J. Nonlinear Anal.: Theory, Methods, and Appl. 29:1997;1343-1351.
5. Dyson J., Villella-Bressan R., Webb G. F. An age and maturity structured model of cell population dynamics. Horn M. A., Simonett G., Webb G. Mathematical Models in Medical and Health Sciences. 1999;99-116 Vanderbilt University Press, Nashville.
6. J. Dyson, R. Villella-Bressan, and, G. F. Webb, A nonlinear age and maturity structured model of population dynamics. II. Chaos, J. Math. Anal. Appl, to appear.
7. Lasota A. Stable and chaotic solutions of a first order partial differential equation. Nonlinear Anal. 5:1981;1181-1193.
8. Lasota A., Mackey M. C. Globally asymptotic properites of proliferating cell populations. J. Math. Biol. 19:1984;43-62.
9. Lasota A., Loskot K., Mackey M. C. Stability properties of proliferatively coupled cell replication models. Acta Biotheor. 39:1991;1-14.
10. Mackey M. C., Dörmer P. Continuous maturation of proliferating erythroid precursors. Cell Tissue Kinet. 15:1982;381-392.
11. Mackey M. C., Rudnicki R. Global stability in a delayed partial differential equation describing cellular replication. J. Math. Biol. 33:1994;89-109.
12. Mackey M. C., Rudnicki R. A new criterion for the global stability of simultaneous cell replication and maturation processes. J. Math. Biol. 38:1999;195-219.
13. Rey A., Mackey M. C. Bifurcations and traveling waves in a delayed partial differential equation. Chaos. 2:1992;231-244.
14. Rey A., Mackey M. C. Multistability and boundary layer development in a transport equation with retarded arguments. Canad. Appl. Math. Quart. 1:1993;1-21.
15. Rey A., Mackey M. C. Transitions and kinematics of reaction-convection fronts in a cell population model. Physica D. 80:1995a;120-139.
16. Rey A., Mackey M. C. Propagation of population pulses and fronts in a cell replication problem: Non-locality and dependence on the initial function. Physica D. 86:1995b;373-395.
17. Yosida K. Functional Analysis. 1965;Springer-Verlag, Berlin.
18. Webb G. F. Logistic models of structured population growth. Comput. Math. Appl. 12A:1986;527-529.
19. Webb G. F. Theory of Nonlinear Age-Dependent Population Dynamics. 1985;Marcel Dekker, New York.
20. Webb G. F. An operator-theoretic formulation of asynchronous exponential growth. Trans. Amer. Math. Soc. 303:1987;751-763.