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

We performed an extensive numerical study of pattern formation scenarios in the two-dimensional Gray-Scott reaction-diffusion model. Ve concentrated o n 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 (spo ts). The traveling one-dimensional autosolitons (wave fronts) can be stable or undergo break-up. The static two-dimensional radially-symmetric autosol ituns may break up and self-replicate leading to the formation of space-fil ling patterns of spots, wave fronts, or spatio-temporal chaos due to the co mpetition of self-replication and annihilation of spots upon collision.