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February  2002, 2(1): 129-147. doi: 10.3934/dcdsb.2002.2.129

Identification of modulated rotating waves in pattern-forming systems with O(2) symmetry

A. Palacios 1,

1. 

Department of Mathematics, San Diego State University, San Diego, CA 92182, United States

Received  April 2001 Revised  October 2001 Published  November 2001

A numerical algorithm for identifying Modulated Rotating Waves in spatially extended systems with O(2) symmetry—the symmetry group of rotations and reflections on the plane, is presented. The algorithm can be applied to numerical simulations of Partial Differential Equations (PDEs) and experimental data obtained in a laboratory. The basic methodology is illustrated with various cellular patterns obtained from video images of a combustion experiment carried out on a circular burner. Rotating waves and modulated rotating waves are successfully identified in the experiment. The algorithm is then validated by comparing the analysis of experimental patterns with the analysis of computational patterns obtained from numerical simulations of a reaction-diffusion PDE model.
Keywords: symmetry., bifurcation theory, Spatio-temporal patterns.
Mathematics Subject Classification: 37M2.
Citation: A. Palacios. Identification of modulated rotating waves in pattern-forming systems with O(2) symmetry. Discrete and Continuous Dynamical Systems - B, 2002, 2 (1) : 129-147. doi: 10.3934/dcdsb.2002.2.129
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