Existence of traveling wavefront for discrete bistable competition model

Chin-Chin Wu

doi:10.3934/dcdsb.2011.16.973

Abstract

We study traveling wavefront solutions for a two-component competition system on a one-dimensional lattice. We combine the monotonic iteration method with a truncation to obtain the existence of the traveling wavefront solution.

Highlights

In this paper, we study the following two-component lattice dynamical system (LDS): duj = + auj (1 − uj − kvj ), dt (1.1) dvj= d(vj+1 + vj−1 − 2vj ) + bvj (1 − vj − huj ), dt where uj = uj (t), vj = vj (t), t ∈ R, j ∈ Z, d > 0, h > 1, k > 1, b > 0 and a > 0.This model arises in the study of strong competition of two species in a habitat which is divided into discrete niches
The unknowns uj, vj are the populations of species u, v at niches j, respectively, constants a, b are the birth rates and h, k are the competition coefficients of species u, v
K > 1 so that these two species are of strong competition

Summary

Introduction

When the former case in Theorem 1.1 occurs, we have the exact tail behavior (U, W )(−∞) = (0, 0) and (U, W )(+∞) = (1, 1) so that we have the existence of a traveling front for our problem. Since the solution of the above truncated problem is discontinuous at x = ±n, it is more convenient to consider the following system of integral equations We prove the following existence result for the truncated problem.

Results

Conclusion