American Institute of Mathematical Sciences

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March  2008, 9(2): 249-266. doi: 10.3934/dcdsb.2008.9.249

Asymptotic behavior of size-structured populations via juvenile-adult interaction

József Z. Farkas 1, and  Thomas Hagen 2,

1. 

Department of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, United Kingdom
2. 

Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, United States

Received  December 2006 Revised  October 2007 Published  December 2007

In this work a size-structured juvenile-adult population model is considered. The linearized dynamical behavior of stationary solutions is analyzed using semigroup and spectral methods. The regularity of the governing linear semigroup allows us to derive biologically meaningful conditions for the linear stability of stationary solutions. The main emphasis in this work is on juvenile-adult interaction and resulting consequences for the dynamics of the system. In addition, we investigate numerically the effect of a non-zero population inflow, due to an external source of newborns, on the linear dynamical behavior of the system in a special case of model ingredients.
Keywords: spectral analysis., linear stability, Structured population dynamics, juvenile-adult intraspecific interaction.
Mathematics Subject Classification: Primary: 92D25, 47D06; Secondary: 35B3.
Citation: József Z. Farkas, Thomas Hagen. Asymptotic behavior of size-structured populations via juvenile-adult interaction. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 249-266. doi: 10.3934/dcdsb.2008.9.249
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