Exact Homoclinic and Heteroclinic Solutions of the Gray-Scott Model for Autocatalysis

@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}
}
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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