Pushed and pulled fronts in a discrete reaction–diffusion equation
| Autor: | Reuben D. O'Dea, John R. King |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Leading edge
Forcing (recursion theory) Coupling strength General Mathematics Mathematical analysis General Engineering Integer lattice Front (oceanography) 010103 numerical & computational mathematics 01 natural sciences Discrete Reaction-Diffusion Equation Liouville-Green Matched-Asymptotic Analysis Travelling Waves 010101 applied mathematics Nonlinear system Classical mechanics Reaction–diffusion system Traveling wave 0101 mathematics Mathematics |
| Zdroj: | Journal of Engineering Mathematics. 102:89-116 |
| ISSN: | 1573-2703 0022-0833 |
| DOI: | 10.1007/s10665-015-9829-3 |
| Popis: | We consider the propagation of wave fronts connecting unstable and stable uniform solutions to a discrete reaction-diffusion equation on a one-dimensional integer lattice. The dependence of the wavespeed on the coupling strength µ between lattice points and on a detuning parameter (α) appearing in a nonlinear forcing is investigated thoroughly. Via asymptotic and numerical studies, the speed both of 'pulled' fronts (whereby the wavespeed can be characterised by the linear behaviour at the leading edge of the wave) and of 'pushed' fronts (for which the nonlinear dynamics of the entire front determine the wavespeed) is investigated in detail. The asymptotic and numerical techniques employed complement each other in highlighting the transition between pushed and pulled fronts under variations of µ and α. |
| Databáze: | OpenAIRE |
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