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.
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- 05.45.-a Nonlinear dynamics and nonlinear dynamical systems
- 47.54,+r Pattern selection; pattern formation
- 82.20.-w Chemical kinetics and dynamics