American Institute of Mathematical Sciences

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January  2008, 9(1): 83-101. doi: 10.3934/dcdsb.2008.9.83

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, United States
2. 

Department of Biostatistical Sciences, Wake Forest University Health Sciences, Medical Center Blvd., Winston Salem, NC 27157, United States

Received  January 2007 Revised  August 2007 Published  October 2007

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.
Keywords: tree dispersion, acceleration in dispersion., traveling wave solution, Coupled map lattice.
Mathematics Subject Classification: Primary: 37N25; Secondary: 92D40 92D25 37L6.
Citation: Miaohua Jiang, Qiang Zhang. A coupled map lattice model of tree dispersion. Discrete & Continuous Dynamical Systems - B, 2008, 9 (1) : 83-101. doi: 10.3934/dcdsb.2008.9.83
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