2004/02/24 by Ernesto M. Nicola, Lutz Brusch, Markus Baer +1
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Spectroscopy and Quantum Chemical Studies #nlin.CD #nlin.PS
paper · pdf · doi:10.1021/jp049213r
published as J. Phys. Chem. B, 108 (38), 14733 -14740, 2004. · 10 pages, 8 figures, submitted to J. Phys. Chem. B on Feb. 20, 2004. A short account of the spiral-antispiral criterion has been given in PRL (see http://link.aps.org/abstract/PRL/v92/e089801)
arxiv created 2004/02/24 · openalex publication_date 2004/09/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Spiral and antispiral waves are studied numerically in two examples of oscillatory reaction−diffusion media and analytically in the corresponding complex Ginzburg−Landau equation (CGLE). We argue that both these structures are sources of waves in oscillatory media, which are distinguished only by the sign of the phase velocity of the emitted waves. Using known analytical results in the CGLE, we obtain a criterion for the CGLE coefficients that predicts whether antispirals or spirals will occur in the corresponding reaction−diffusion systems. We apply this criterion to the FitzHugh−Nagumo and Brusselator models by deriving the CGLE near the Hopf bifurcations of the respective equations. Numerical simulations of the full reaction−diffusion equations confirm the validity of our simple criterion near the onset of oscillations. They also reveal that antispirals often occur near the onset and turn into spirals further away from it. The transition from antispirals to spirals is characterized by a divergence in the wavelength. A tentative interpretation of recent experimental observations of antispiral waves in the Belousov−Zhabotinsky reaction in a microemulsion is given.