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.
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Received 6 November 2000 and Received in final form 27 February 2001
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Muratov, C., Osipov, V. Spike autosolitons and pattern formation scenarios in the two-dimensional Gray-Scott model. Eur. Phys. J. B 22, 213–221 (2001). https://doi.org/10.1007/s100510170129
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DOI: https://doi.org/10.1007/s100510170129