| 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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