Szymon Cygan

Non local toy model of patterns formation.

We study a pattern formation described by certain non local evolution equation. This evolution equation was obtained by a modification of a model introduced by Shigeru Kondo to explain colour pattern on a skin of guppy fish. We prove the existence of stationary solutions in the linear and non linear case either using the bifurcation theory or Schauder fix point theorem. We also present numerical studies of this model and show that it exhibits patterns similar to those obtained by Kondo.