American Institute of Mathematical Sciences

Advanced
November  2009, 12(4): 883-904. doi: 10.3934/dcdsb.2009.12.883

Spreading speed and traveling wavefront of an age-structured population diffusing in a 2D lattice strip

Peixuan Weng 1,

1. 

School of Mathematics, South China Normal University, Guangzhou 510631, China

Received  July 2008 Revised  April 2009 Published  August 2009

We derive an age-structured population model for the growth of a single species on a 2-dimensional (2D) lattice strip with Neumann boundary conditions. We show that the dynamics of the mature population is governed by a lattice reaction-diffusion system with delayed global interaction. Using theory of asymptotic speed of spread and monotone traveling waves for monotone semiflows, we obtain the asymptotic speed of spread $c^$*, the nonexistence of traveling wavefronts with wave speed $0 < c < c^$*, and the existence of traveling wavefront connecting the two equilibria $w\equiv 0$ and $w\equiv w^+$ for $c\geq c^$*.
Keywords: monotone semiflow, 2D lattice strip., lattice system, age-structured population model, traveling wavefront, spreading speed.
Mathematics Subject Classification: Primary: 34K31, 34K25; Secondary: 92D2.
Citation: Peixuan Weng. Spreading speed and traveling wavefront of an age-structured population diffusing in a 2D lattice strip. Discrete and Continuous Dynamical Systems - B, 2009, 12 (4) : 883-904. doi: 10.3934/dcdsb.2009.12.883
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