UNSPECIFIED (2000) Target patterns and spirals in planar reaction-diffusion systems. JOURNAL OF NONLINEAR SCIENCE, 10 (3). pp. 333-354. ISSN 0938-8974

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Abstract

Solutions of reaction-diffusion equations on a circular domain are considered. With Robin boundary conditions, the primary instability may be a Hopf bifurcation with eigenfunctions exhibiting prominent spiral features. These eigenfunctions, defined by Bessel functions of complex argument, peak near the boundary and are called wall modes. In contrast, if the boundary conditions are Neumann or Dirichlet, then the eigenfunctions are defined by Bessel functions of real argument, and take the form of body modes filling the interior of the domain. Body modes typically do not exhibit pronounced spiral structure. We argue that the wall modes are important for understanding the formation process of spirals, even in extended systems. Specifically, we conjecture that wall modes describe the core of the spiral; the constant-amplitude spiral visible outside the core is the result of strong nonlinearities which enter almost immediately above threshold as a consequence of the exponential radial growth of the wall modes.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery Q Science > QC Physics
Journal or Publication Title:	JOURNAL OF NONLINEAR SCIENCE
Publisher:	SPRINGER VERLAG
ISSN:	0938-8974
Date:	May 2000
Volume:	10
Number:	3
Number of Pages:	22
Page Range:	pp. 333-354
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/13456

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