Fourier-Bessel analysis of patterns in a circular domain

This paper explores the use of the Fourier-Bessel analysis for characterizing patterns in a circular domain. A set of stable patterns is found to be well-characterized by the Fourier-Bessel functions. Most patterns are dominated by a principal Fourier-Bessel mode [n, m] which has the largest Fourier-Bessel decomposition amplitude when the control parameter R is close to a corresponding non-trivial root (ρ_n,m) of the Bessel function. Moreover, when the control parameter is chosen to be close to two or more roots of the Bessel function, the corresponding principal Fourier-Bessel modes compete to dominate the morphology of the patterns.