{
  "id": "1511.01414",
  "version": "v1",
  "published": "2015-11-04T17:47:15.000Z",
  "updated": "2015-11-04T17:47:15.000Z",
  "title": "Global bifurcation diagram of steady states of systems of PDEs via rigorous numerics: a 3-component reaction-diffusion system",
  "authors": [
    "Maxime Breden",
    "Jean-Philippe Lessard",
    "Matthieu Vanicat"
  ],
  "categories": [
    "math.DS",
    "math.AP"
  ],
  "abstract": "In this paper, we use rigorous numerics to compute several global smooth branches of steady states for a system of three reaction-diffusion PDEs introduced by Iida et al. [J. Math. Biol., {\\bf 53}, 617--641 (2006)] to study the effect of cross-diffusion in competitive interactions. An explicit and mathematically rigorous construction of a global bifurcation diagram is done, except in small neighborhoods of the bifurcations. The proposed method, even though influenced by the work of van den Berg et al. [Math. Comp., {\\bf 79}, 1565--1584 (2010)], introduces new analytic estimates, a new {\\em gluing-free} approach for the construction of global smooth branches and provides a detailed analysis of the choice of the parameters to be made in order to maximize the chances of performing successfully the computational proofs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-04T17:47:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global bifurcation diagram",
      "steady states",
      "rigorous numerics",
      "reaction-diffusion system",
      "global smooth branches"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}