Eur. Phys. J. B 22, 213-221 (2001)
https://doi.org/10.1007/s100510170129

Spike autosolitons and pattern formation scenarios in the two-dimensional Gray-Scott model

¹ Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
² CSIC, Laboratorio de Fisica de Sistemas Pequeños y Nanotecnologia, Calle Serrano, 144, 28006, Madrid, Spain

Corresponding author: ^a muratov@m.njit.edu

Received: 6 November 2000
Revised: 27 February 2001
Published online: 15 July 2001

Abstract

We performed an extensive numerical study of pattern formation scenarios in the two-dimensional Gray-Scott reaction-diffusion model. We concentrated on the parameter region in which there exists a strong separation of length and/or time scales. We found that the static one-dimensional autosolitons (stripes) break up into two-dimensional radially-symmetric autosolitons (spots). The traveling one-dimensional autosolitons (wave fronts) can be stable or undergo breakup. The static two-dimensional radially-symmetric autosolitons may break up and self-replicate leading to the formation of space-filling patterns of spots, wave fronts, or spatio-temporal chaos due to the competition of self-replication and annihilation of spots upon collision.