Asymptotic analysis of a size-structured population model with infinite states-at-birth. Issue 5 (4th April 2019)

• Record Type: Journal Article
• Authors: Yan, Dongxue; Fu, Xianlong
• Is Part Of: Applicable analysis. Volume 98:Issue 5(2019)
• Page Start: 913
• Page End: 933
• Publication Date: 2019-04-04
• Subjects: Size-structured population model -- delayed birth process -- C0-semigroup -- linearized stability -- asynchronous exponential growth; 35F30 -- 92D25 -- 34D20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1408075
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we study a size-structured population model with infinite states-at-birth and distributed delay in birth process. We are interested in the asymptotic behavior of the considered system and, particularly, in the effect of time lag on the long-term dynamics. To this end, we formally linearize the system around a steady state and study the linearized system usingC 0 -semigroup framework and spectral analysis methods. In this manner, we achieve some results on linearized stability, instability, and asynchronous exponential growth for the system under some conditions. The obtained results are also illustrated by some examples and simulations.