A size structured model of cell

Discrete and Continuous Dynamical Systems - Series B

Volumn 1, Issue 4, 2001, Pages 471-484

  Howard, Dwarfism Keith E ^a  

^a KENYON COLLEGE   (United States)

Author keywords

Population dynamics; Semigroups of operators; Topological transitive

Indexed keywords

EID: 0346338593     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2001.1.471     Document Type: Article

References (22)

1. D.J. Bacon, Anemia, in Ambulatory Care, Mirram Rabkia, 1997.
2. G.I. Bell, E.G. Anderson, Cell Growth and Division I. A Mathematical Model with Applications to Cell Volume Distributions in Mamilian Suspension Cultures, Biophysics Journal 7 1967, 329-351.
3. Buss, Normal and Abnormal Hemoglobin Synthesis, Core B Hematology, Wake Forest University Medical Center, Lecture Notes, 1997.
4. W. Desch, W. Schappacher, G.F. Webb, Hypercyclic and Chaotic Semigroups of Linear Operators, Ergodic Theory and Dynamical Systems, 17 1997, 793-819.
5. R. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, 1989.
6. O. Diekmann, H.J.A.M. Heijmans, U.R. Thieme, On the Stability of the Cell Size Distribution, J. Math. Biol. 19 1984, 227-248.
7. O. Diekmann, H.A. Lauwerier, T. Aldenberg, J.A.J. Metz, Growth, Fission, and the Stable Size Distribution, J. Math. Biol. 18 1983, 135-148.
8. J. Dyson, R. Villella-Bressan, and G.F. Webb, An Age and Maturity Structured Model of Cell Population Dynamics, in "Mathematical Models in Medical and Health Sciences", (Mary Ann Horn, Gieri Simonett, and Glenn Webb, Eds.) Vanderbilt University Press, Nashville TN ISBN 0-8265-1310-7.
9. A.G. Fredrickson, D. Ramkrishna, U.M. Tsuchiya, Statistics and Dynamics of Procaryotic Cell Populations, Math. Biosc. 1 1967, 327-374.
10. G. Geiner, R. Nagel, Growth of Cell Populations via One Parameter Semigroups of Positive Operators, Mathematics Applied to Science 1988, 79-104.
11. Georgia Division of Public Health, Newborn Screening Manuel, Georgia Department of Public Human Resources, Division of Public Health, 1998.
12. J.A. Goldstein, Semigroups of Operators and Applications, Oxford University Press, 1985.
13. A. Grabosch, H.J.A.M. Heijmans, Production, Developement, and Maturation of Red Blood Cels: A Mathematical Model, in Mathematical Population Dynamics, Lecture Notes in Pure and Applied Mathematics 131 1991, 189-210.
14. K. Howard, Size and Maturity Structured Models of Cell Population Dynamics Exhibiting Chaotic Behavior, Dissertation, Vanderbilt University.
15. J.A.J. Metz, O. Diekmann, The Dynamics of Physiologically Structured Populations, Lecture Notes in Biomathematics, 68, Springer-Verlag, 1986.
16. H. Miyata, M. Miyata, M. Ito, Cell-Cycle in Fission Yeast, Schizosaccharomyces Pombe. I. Relationship Between Cell Size and Cycle Time, Cell Struct. Funct. 3 1978, 39-46.
17. P.G. Painter, A.G Marr, Mathematics of Microbial Populations, Ann. Rev. Microbiol. 22 1968, 519-548.
18. W. Rudin, Real and Complex Analysis, McGraw-Hill, New York third edition, 1987.
19. J.W. Sinko, W. Streifer, A Model for Age-Size Structure of a Population, Ecology 48 1967, 910-918.
20. J.W. Sinko, W. Streifer, A Model for Population Reproducing by Fission, Ecology 52, 330-335.
21. J.J. Tyson, O. Diekmann, Sloppy Size Control of the Cell Division Cycle, J. Theor. Biol. 1986.
22. G.F. Webb, Random Transitions, Size Control, and Inheritance in Cell Population Dynamics, Mathematical Biosciences, 84 Eiservier Science Publishing CO., Inc., 1987.