Homoclinic Stripe Patterns

  title={Homoclinic Stripe Patterns},
  author={Arjen Doelman and Harmen van der Ploeg},
  journal={SIAM J. Applied Dynamical Systems},
In this paper, we study homoclinic stripe patterns in the two-dimensional generalized Gierer– Meinhardt equation, where we interpret this equation as a prototypical representative of a class of singularly perturbed monostable reaction-diffusion equations. The structure of a stripe pattern is essentially one-dimensional; therefore, we can use results from the literature to establish the existence of the homoclinic patterns. However, we extend these results to a maximal domain in the parameter… CONTINUE READING


Publications citing this paper.
Showing 1-10 of 35 extracted citations


Publications referenced by this paper.
Showing 1-10 of 43 references

A stability index analysis of 1-D patterns of the Gray–Scott model, Mem

  • A. Doelman, R. A. Gardner, T. J. Kaper
  • Amer. Math. Soc.,
  • 2002
Highly Influential
10 Excerpts

Large stable pulse solutions in reaction-diffusion equations

  • A. Doelman, R. A. Gardner, T. J. Kaper
  • Indiana Univ. Math. J.,
  • 2001
Highly Influential
10 Excerpts

A skeleton structure for self-replication dynamics

  • Y. Nishiura, D. Ueyama
  • Phys. D,
  • 1999
Highly Influential
7 Excerpts

A topological invariant arising in the stability of traveling waves

  • J. Alexander, R. A. Gardner, C.K.R.T. Jones
  • J. Reine Angew. Math.,
  • 1990
Highly Influential
4 Excerpts

The stability of spike solutions of the one-dimensional Gierer

  • D. Iron, M. J. Ward, J. Wei
  • Meinhardt model, Phys. D,
  • 2001
Highly Influential
5 Excerpts

Point condensation generated by a reaction-diffusion system in axially symmetric domains, Japan

  • W.-M. Ni, I. Takagi
  • J. Indust. Appl. Math.,
  • 1995
Highly Influential
4 Excerpts

Ponce-Dawson, Dynamics of self-replicating patterns in reaction diffusion systems

  • W. N. Reynolds, J. E. Pearson
  • Phys. Rev. Lett.,
  • 1994
Highly Influential
5 Excerpts

Similar Papers

Loading similar papers…