|Appears in Collections:||Computing Science and Mathematics Journal Articles|
|Peer Review Status:||Refereed|
|Title:||On a size-structured two-phase population model with infinite states-at-birth|
|Author(s):||Farkas, Jozsef Zoltan|
asynchronous exponential growth
Animal populations Mathematical models
|Citation:||Farkas JZ & Hinow P (2010) On a size-structured two-phase population model with infinite states-at-birth. Positivity, 14 (3), pp. 501-514. https://doi.org/10.1007/s11117-009-0033-4|
|Abstract:||In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an "active" phase when individuals grow, reproduce and die and a second "resting" phase when individuals only grow. Transition between these two phases depends on individuals' size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.|
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