Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

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

Pages: 249 - 266, Volume 9, Issue 2, March 2008      doi:10.3934/dcdsb.2008.9.249

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József Z. Farkas - Department of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, United Kingdom (email)
Thomas Hagen - Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, United States (email)

Abstract: 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:  Structured population dynamics, juvenile-adult intraspecific interaction, linear stability, spectral analysis.
Mathematics Subject Classification:  Primary: 92D25, 47D06; Secondary: 35B35.

Received: December 2006;      Revised: October 2007;      Available Online: December 2007.