52 citations · 54 across the 6 of their papers we have counts for
4 papers · 1 filter
Twisted and Nontwisted Bifurcations Induced by Diffusion
Xiao-Biao Lin
We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loo…
Shadowing matching errors for wave-front-like solutions
Xiao-Biao Lin
Consider a singularly perturbed system Assume that the system has a sequence of regular and internal lay…
Local and Global Existence of Multiple Waves Near Formal Approximations
Xiao-Biao Lin
Assuming that a formal approximation of multiple waves has been obtained by matched asymptotic methods, we derive a {\em Spatial Shadowing lemma} to construct exact solutions near…
Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system
Xiao-Biao Lin
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymp…