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Volume 5, Number 1, 2015, Pages 64-76                                                                DOI:10.11948/2015006
Traveling wavefronts of a delayed lattice reaction-diffusion model
Li Shu,Peixuan Weng,Yanling Tian
Keywords:Pioneer-climax model, lattice differential system, harmless delay, traveling wave solution, minimal wave speed.
Abstract:
      We investigate a system of delayed lattice differential system which is a model of pioneer-climax species distributed on one dimensional discrete space. We show that there exists a constant $c^*>0$, such that the model has traveling wave solutions connecting a boundary equilibrium to a co-existence equilibrium for $c\geq c^*$. We also argue that $c^*$ is the minimal wave speed and the delay is harmless. The Schauder's fixed point theorem combining with upper-lower solution technique is used for showing the existence of wave solution.
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