Asymptotic behavior of a nonlinear functional-integral equation of cell kinetics with unequal division Journal Article
| Authors: | Arino, O.; Kimmel, M. |
| Article Title: | Asymptotic behavior of a nonlinear functional-integral equation of cell kinetics with unequal division |
| Abstract: | A model of cell cycle kinetics is proposed, which includes unequal division of cells, and a nonlinear dependence of the fraction of cells re-entering proliferation on the total number of cells in the cycle. The model is described by a nonlinear functional-integral equation. It is analyzed using the operator semigroup theory combined with classical differential equations approach. A complete description of the asymptotic behavior of the model is provided for a relatively broad class of nonlinearities. The nonnegative solutions either tend to a stable steady state, or to zero. The simplicity of the model makes it an interesting step in the analysis of dynamics of nonlinear structure populations. © 1989 Springer-Verlag. |
| Keywords: | cell cycle; biological model; models, biological; cell kinetics; article; support, non-u.s. gov't; support, u.s. gov't, p.h.s.; functional-integral equation; operator semigroup |
| Journal Title: | Journal of Mathematical Biology |
| Volume: | 27 |
| Issue: | 3 |
| ISSN: | 0303-6812 |
| Publisher: | Springer |
| Date Published: | 1989-05-01 |
| Start Page: | 341 |
| End Page: | 354 |
| Language: | English |
| DOI: | 10.1007/bf00275817 |
| PUBMED: | 2746142 |
| PROVIDER: | scopus |
| DOI/URL: | |
| Notes: | Article -- Export Date: 14 April 2020 -- Source: Scopus |
