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Bounds on the hausdorff dimension of a renormalisation map arising from an excitable reaction-diffusion system on a fractal lattice

Mulholland, A.J. (2008) Bounds on the hausdorff dimension of a renormalisation map arising from an excitable reaction-diffusion system on a fractal lattice. Chaos, Solitons and Fractals, 35 (2). pp. 274-284. ISSN 0960-0779

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    Abstract

    A renormalisation approach to investigate travelling wave solutions of an excitable reaction- diusion system on a deterministic fractal structure has recently been derived. The dynamics of a particular class of solutions which are governed by a two dimensional subspace of these renormalisation recursion relationships are discussed in this paper. The bifurcations of this mapping are discussed with reference to the discontinuities which arise at the singularities. The map is chaotic for a bounded region in parameter space and bounds on the Hausdor dimension of the associated invariant hyperbolic set are calculated.

    Item type: Article
    ID code: 13526
    Keywords: Hausdorff dimension, renormalisation map, reaction-diffusion system, fractal lattice, Mathematics, Mathematics(all)
    Subjects: Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
    Depositing user: Mrs Mary McAuley
    Date Deposited: 14 Jan 2010 11:14
    Last modified: 04 Sep 2014 23:59
    URI: http://strathprints.strath.ac.uk/id/eprint/13526

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