Bifurcation in a a Reaction Diffusion System

Author: Bissett, Edward J.

Year: 1978

Degree: Dissertation (Ph.D.)

Advisor: Cohen, Donald S.

Committee Member: Unknown, Unknown

Option: Applied Mathematics

DOI: 10.7907/zvxr-9880

Abstract

The bifurcation and nonlinear stability properties of the Meinhardt-Gierer model for biochemical pattern formation are studied. Analyses are carried out in parameter ranges where the linearized system about a trivial solution loses stability through one to three eigenfunctions, yielding both time independent and periodic final states. Solution branches are obtained that exhibit secondary bifurcation and imperfection sensitivity and that appear, disappear, or detach themselves from other branches.

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