✦ LIBER ✦

A simple method of parameter space determination for diffusion-driven instability with three species

✍ Scribed by Hong Qian; J.D. Murray

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 451 KB
Volume: 14
Category: Article
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(00)00169-5

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✦ Synopsis

A very simple, practical, necesssry and sufficient condition for diffusion-driven linear instability and parameter space determination in nonlinear reaction systems with three species is presented. With respect to the stability matrix A from linearization near a stable steady-state of a reaction system, two necessary conditions are given: (i) A is stable but not negative definite; and (ii) either the largest diagonal elements of A is positive or the smallest diagonal cofactors of A is negative. Condition (i) can be generalized to any number of species but (ii) is a stronger condition which, in fact, is shown to be sufficient for diffusion-driven instability. As an example, the result is applied to the three-species Oregonator, the model for the Belousov-Zhabotinsky reaction.

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