Pod systems: an equivariant ordinary differential equation approach to dynamical systems on a spatial domain

Elmhirst, Toby, Stewart, Ian, and Doebeli, Michael (2008) Pod systems: an equivariant ordinary differential equation approach to dynamical systems on a spatial domain. Nonlinearity, 21 (7). pp. 1507-1531.

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Abstract

We present a class of systems of ordinary differential equations (ODEs), which we call 'pod systems', that offers a new perspective on dynamical systems defined on a spatial domain. Such systems are typically studied as partial differential equations, but pod systems bring the analytic techniques of ODE theory to bear on the problems, and are thus able to study behaviours and bifurcations that are not easily accessible to the standard methods. In particular, pod systems are specifically designed to study spatial dynamical systems that exhibit multi-modal solutions.

Item ID: 6965
Item Type: Article (Refereed Research - C1)
Keywords: spatial dynamical systems; permutational symmetry
ISSN: 1361-6544
Date Deposited: 09 Apr 2010 04:56
FoR Codes: 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems @ 60%
01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010105 Group Theory and Generalisations @ 20%
01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications @ 20%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 100%
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