caa a22 4500 47580533X CHVBK 20180406123745.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1007/s003329910013 doi (NATIONALLICENCE)springer-10.1007/s003329910013 Target Patterns and Spirals in Planar Reaction-Diffusion Systems [Elektronische Daten] [M. Golubitsky, E. Knobloch, I. Stewart] wall: modes. In contrast, if the boundary conditions are Neumann or Dirichlet, then the eigenfunctions are defined by Bessel functions of real argument, and take the form of body modes filling the interior of the domain. Body modes typically do not exhibit pronounced spiral structure. We argue that the wall modes are important for understanding the formation process of spirals, even in extended systems. Specifically, we conjecture that wall modes describe the core of the spiral; the constant-amplitude spiral visible outside the core is the result of strong nonlinearities which enter almost immediately above threshold as a consequence of the exponential radial growth of the wall modes. Springer-Verlag New York Inc., 2000 Golubitsky M. Department of Mathematics, University of Houston, Houston, TX 77204-3476, USA, US aut Knobloch E. Department of Physics, University of California, Berkeley, CA 94720, USA, US aut Stewart I. Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK, GB aut Journal of Nonlinear Science Springer-Verlag 10/3(2000-06-01), 333-354 0938-8974 10:3<333 2000 10 332 https://doi.org/10.1007/s003329910013 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003329910013 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Golubitsky M. Department of Mathematics, University of Houston, Houston, TX 77204-3476, USA, US aut NATIONALLICENCE 700 1- Knobloch E. Department of Physics, University of California, Berkeley, CA 94720, USA, US aut NATIONALLICENCE 700 1- Stewart I. Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK, GB aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 10/3(2000-06-01), 333-354 0938-8974 10:3<333 2000 10 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer