## Rigorous Numerics for Symmetric Connecting Orbits: Even Homoclinics of the Gray-Scott Equation

- Jan Bouwe van den Berg, Jason D. Mireles-James, Jean-Philippe Lessard, Konstantin Mischaikow
- SIAM J. Math. Analysis
- 2011

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@article{Hale2000ExactHA, title={Exact Homoclinic and Heteroclinic Solutions of the Gray-Scott Model for Autocatalysis}, author={J. K. Hale and L. A. Peletier and William C. Troy}, journal={SIAM Journal of Applied Mathematics}, year={2000}, volume={61}, pages={102-130} }

- Published 2000 in SIAM Journal of Applied Mathematics
DOI:10.1137/S0036139998334913

In this paper we obtain explicit nontrivial stationary patterns in the one-dimensional Gray–Scott model for cubic autocatalysis. Involved in the reaction are two chemicals, A and B, whose diffusion coefficients are denoted by DA and DB , respectively. The chemical A is fed into the system at a rate kf , reacts with the catalyst B at a rate k1, and the catalyst decays at a rate k2. If these parameters obey the relation (∗) kf/DA = k2/DB , then, for appropriate values of the rate constants, we… CONTINUE READING

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