|Appears in Collections:||Computing Science and Mathematics Journal Articles|
|Peer Review Status:||Refereed|
|Title:||Asymptotic analysis of a size-structured cannibalism model with infinite dimensional environmental feedback|
|Authors:||Farkas, Jozsef Zoltan|
linear semigroup methods
asynchronous exponential growth
|Publisher:||American Institute of Mathematical Sciences (AIMS)|
|Citation:||Farkas JZ & Hagen T (2009) Asymptotic analysis of a size-structured cannibalism model with infinite dimensional environmental feedback, Communications on Pure and Applied Analysis, 8 (6), pp. 1825-1839.|
|Abstract:||In this work we consider a size-structured cannibalism model with the model ingredients (fertility, growth, and mortality rate) depending on size (ranging over an infinite domain) and on a general function of the standing population (environmental feedback). Our focus is on the asymptotic behavior of the system, in particular on the effect of cannibalism on the long-term dynamics. To this end, we formally linearize the system about steady state and establish conditions in terms of the model ingredients which yield uniform exponential stability of the governing linear semigroup. We also show how the point spectrum of the linearized semigroup generator can be characterized in the special case of a separable attack rate and establish a general instability result. Further spectral analysis allows us to give conditions for asynchronous exponential growth of the linear semigroup.|
|Rights:||The publisher does not allow this work to be made publicly available in this Repository. 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.|
|Affiliation:||Computing Science - CSM Dept|
University of Memphis
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