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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Steady states in hierarchical structured populations with distributed states at birth
Author(s): Farkas, Jozsef Zoltan
Hinow, Peter
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Keywords: Hierarchical structured populations, steady states, fixed points of nonlinear maps, semigroups of linear operators, spectral methods, stability
Issue Date: Nov-2012
Date Deposited: 26-Sep-2012
Citation: Farkas JZ & Hinow P (2012) Steady states in hierarchical structured populations with distributed states at birth. Discrete and Continuous Dynamical Systems - Series B, 17 (8), pp. 2671-2689.
Abstract: We investigate steady states of a quasilinear first order hyperbolic partial integro-differential equation. The model describes the evolution of a hierarchical structured population with distributed states at birth. Hierarchical size-structured models describe the dynamics of populations when individuals experience size-specific environment. This is the case for example in a population where individuals exhibit cannibalistic behavior and the chance to become prey (or to attack) depends on the individual's size. The other distinctive feature of the model is that individuals are recruited into the population at arbitrary size. This amounts to an infinite rank integral operator describing the recruitment process. First we establish conditions for the existence of a positive steady state of the model. Our method uses a fixed point result of nonlinear maps in conical shells of Banach spaces. Then we study stability properties of steady states for the special case of a separable growth rate using results from the theory of positive operators on Banach lattices.
DOI Link: 10.3934/dcdsb.2012.17.2671
Rights: This item has been embargoed for a period. During the embargo please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series B following peer review. The definitive publisher-authenticated version Volume 17, Issue 8, November 2012 Pages: 2671 - 2689, is available online at:

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