Title: Bifurcation of co-existing traveling wave solutions in a three-component competition–diffusion system
Abstract:We analyze the bifurcation structure of co-existing traveling wave solutions of a three-component competition–diffusion system that models an exotic competing species W invading the native system of s...We analyze the bifurcation structure of co-existing traveling wave solutions of a three-component competition–diffusion system that models an exotic competing species W invading the native system of strongly competing species U and V. By combining spectral analysis with center manifold reductions, the following are shown: The trivial traveling wave solution without W is destabilized at the critical intrinsic growth rate of W, and its linearized operator has two types of degeneracies. For each case, new co-existing traveling wave solutions bifurcate trans-critically from the trivial one, with the intrinsic growth rate of W as a bifurcation parameter. The stability of each solution is also determined through the normal forms on center manifolds.Read More