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Computation of spiral spectra. (English) Zbl 1093.35014
Summary: A computational linear stability analysis of spiral waves in a reaction-diffusion equation is performed on large disks. As the disk radius $R$ increases, the eigenvalue spectra converge to the absolute spectrum predicted by Sandstede and Scheel. The convergence rate is consistent with $1/R$, except possibly near the edge of the spectrum. Eigenfunctions computed on large disks are compared with predicted exponential forms. Away from the edge of the absolute spectrum the agreement is excellent, while near the edge computed eigenfunctions deviate from predictions, probably due to finite-size effects. In addition to eigenvalues associated with the absolute spectrum, computations reveal point eigenvalues. The point eigenvalues and associated eigenfunctions responsible for both core and far-field break-up of spiral waves are shown.

35B30Dependence of solutions of PDE on initial and boundary data, parameters
35K57Reaction-diffusion equations
74J30Nonlinear waves (solid mechanics)
92C99Physiological, cellular and medical topics
35P20Asymptotic distribution of eigenvalues and eigenfunctions for PD operators
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