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 (ρn,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.