Localized Patterns in Reaction-Diffusion Systems
Open Access
- 1 January 1980
- journal article
- Published by Oxford University Press (OUP) in Progress of Theoretical Physics
- Vol. 63 (1), 106-121
- https://doi.org/10.1143/ptp.63.106
Abstract
A new chemical pattern is discussed, which is a propagationless solitary island in an infinite medium. We demonstrate analytically its existence and stability for a certain simple model. The localization turns out to be a consequence of the rapid diffusion of an inhibiting substance occurring in a potentially excitable system. In order to extract the important features of the localized pattern, the method of singular perturbation is employed, with the following results: (1) A stable motionless solitary pattern can exist either for a monostable or bistable system. (2) Under suitable conditions such a pattern undergoes the Hopf bifurcation, leading to a “breathing motion” of the activated droplet. The analysis is restricted to the one-dimensional case throughout.Keywords
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