Stability and instability in the Gray-Scott model: The case of equal diffusivities

We prove that a family of explicit stationary homoclinic orbits of the Gray-Scott system of cubic autocatalysis is unstable, and that an explicit heteroclinic orbit of this system is asymptotically, and exponentially stable.

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Bibliographic Details
Published in:Applied mathematics letters 1999, Vol.12 (4), p.59-65
Main Authors: Hale, J.K., Peletier, L.A., Troy, W.C.
Format: Article
Language:English
Subjects:
Gray-Scott model
Heteroclinic orbits
Homoclinic orbits
Reaction-diffusion equations
Stability
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Summary:We prove that a family of explicit stationary homoclinic orbits of the Gray-Scott system of cubic autocatalysis is unstable, and that an explicit heteroclinic orbit of this system is asymptotically, and exponentially stable.
ISSN:0893-9659
1873-5452
DOI:10.1016/S0893-9659(99)00035-X