TY - JOUR
T1 - On Spiral Waves Arising in Natural Systems
AU - D. Bini, C. Cherubini, S. Filippi, A. Gizzi & P. E. Ricci
JO - Communications in Computational Physics
VL - 3
SP - 610
EP - 622
PY - 2010
DA - 2010/08
SN - 8
DO - http://doi.org/10.4208/cicp.240909.170210a
UR - https://global-sci.org/intro/article_detail/cicp/7587.html
KW - 
AB - <p style="text-align: justify;">Spiral waves appear in many different natural contexts: excitable biological
tissues, fungi and amoebae colonies, chemical reactions, growing crystals, fluids and
gas eddies as well as in galaxies. While the existing theories explain the presence of
spirals in terms of nonlinear parabolic equations, it is explored here the fact that self-sustained
spiral wave regime is already present in the linear heat operator, in terms of
integer Bessel functions of complex argument. Such solutions, even if commonly not
discussed in the literature because diverging at spatial infinity, play a central role in the
understanding of the universality of spiral process. In particular, we have studied how
in nonlinear reaction-diffusion models the linear part of the equations determines the
wave front appearance while nonlinearities are mandatory to cancel out the blowup
of solutions. The spiral wave pattern still requires however at least two cross-reacting
species to be physically realized. Biological implications of such a results are discussed.</p>