2018/12/19 by Robbin Bastiaansen, Bastiaansen, Robbin, Martina Chirilus‐Bruckner +3 · 4 citations
Mathematics · Medicine · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.1812.07804
openalex publication_date 2018/12/19 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28
Motivated by its application in ecology, we consider an extended Klausmeier\nmodel, a singularly perturbed reaction-advection-diffusion equation with\nspatially varying coefficients. We rigorously establish existence of stationary\npulse solutions by blending techniques from geometric singular perturbation\ntheory with bounds derived from the theory of exponential dichotomies.\nMoreover, the spectral stability of these solutions is determined, using\nsimilar methods. It is found that, due to the break-down of translation\ninvariance, the presence of spatially varying terms can stabilize or\ndestabilize a pulse solution. In particular, this leads to the discovery of a\npitchfork bifurcation and existence of stationary multi-pulse solutions.\n