Spike autosolitons and pattern formation scenarios in the two-dimensional Gray-Scott model |
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Authors: | C.B. Muratov V.V. Osipov |
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Affiliation: | (1) Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA, US;(2) CSIC, Laboratorio de Fisica de Sistemas Peque nos y Nanotecnologia, Calle Serrano, 144, 28006, Madrid, Spain, ES |
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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. Received 6 November 2000 and Received in final form 27 February 2001 |
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Keywords: | PACS. 47.54.+rPattern selection pattern formation – 82.20.-wChemical kinetics and dynamics – 05.45.-a |
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