On Spiral Waves Arising in Natural Systems (Communications in Computational Physics, 2010)
Spiral waves appear in many different natural contexts: excitable biologicaltissues, fungi and amoebae colonies, chemical reactions, growing crystals, fluids andgas eddies as well as in galaxies. While the existing theories explain the presence ofspirals in terms of nonlinear parabolic equations, it is explored here the fact that self-sustainedspiral wave regime is already present in the linear heat operator, in terms ofinteger Bessel functions of complex argument. Such solutions, even if commonly notdiscussed in the literature because diverging at spatial infinity, play a central role in theunderstanding of the universality of spiral process. In particular, we have studied howin nonlinear reaction-diffusion models the linear part of the equations determines thewave front appearance while nonlinearities are mandatory to cancel out the blowupof solutions. The spiral wave pattern still requires however at least two cross-reactingspecies to be physically realized. Biological implications of such a results are discussed.