A coupled map lattice model of tree dispersion

Miaohua Jiang; Qiang Zhang

doi:10.3934/dcdsb.2008.9.83

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2008, Volume 9, Issue 1: 83-101. Doi: 10.3934/dcdsb.2008.9.83

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A coupled map lattice model of tree dispersion

Miaohua Jiang^1, and
Qiang Zhang^2,

1.
Department of Mathematics, Wake Forest University, Winston Salem, NC 27109
2.
Department of Biostatistical Sciences, Wake Forest University Health Sciences, Medical Center Blvd., Winston Salem, NC 27157

Received: December 31, 2006

Revised: July 31, 2007

Published: December 2007

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Abstract

We study the coupled map lattice model of tree dispersion. Under quite general conditions on the nonlinearity of the local growth function and the dispersion (coupling) function, we show that when the maximal dispersal distance is finite and the spatial redistribution pattern remains unchanged in time, the moving front will always converge in the strongest sense to an asymptotic state: a traveling wave with finite length of the wavefront. We also show that when the climate becomes more favorable to growth or germination, the front at any nonzero density level will have a positive acceleration. An estimation of the magnitude of the acceleration is given.

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Mathematics Subject Classification: Primary: 37N25; Secondary: 92D40 92D25 37L60.

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