(In)Stability of Travelling Waves in a Model of Haptotaxis

Abstract

We examine the spectral stability of travelling waves of the haptotaxis model studied in Harley et al (2014a). In the process we apply Liénard coordinates to the linearised stability problem and use a Riccati-transform/Grassmanian spectral shooting method á la Harley et al (2015), Ledoux et al (2009) and Ledoux et al (2010) in order to numerically compute the Evans function and point spectrum of a linearised operator associated with a travelling wave. We numerically show the instability of non-monotone waves (type IV) and the stability of the monotone ones (types I-III) to perturbations in an appropriately weighted space.

24 pages, 8 figures; expanded introduction and discussion, updated figures for consistency, results unchanged 26 pages, 8 figures; expanded references and text, results and figures unchanged 26 pages, 8 figures; final revisions, results and figures unchanged