Kodai Mathematical Journal

Unstable subsystems cause Turing instability

Atsushi Anma, Kunimochi Sakamoto, and Tohru Yoneda

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Abstract

We study Turing instabilities in 3-component reaction-diffusion systems. The existence of a complementary pair of stable-unstable subsystems always gives rise to Turing instability for suitable diagonal diffusion matrices. There are two types of Turing instability, one called steady instability and the other wave instability. To determine which of the two types of instability actually occurs, easily verifiable conditions on unstable subsystems are given. A complementary pair of unstable-unstable subsystems in a stable full system also leads to steady instability. Our results give a perspective to the rich variety and complexity of pattern dynamics in 3-component systems of reaction-diffusion equations at the onset.

Article information

Source
Kodai Math. J., Volume 35, Number 2 (2012), 215-247.

Dates
First available in Project Euclid: 4 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1341401049

Digital Object Identifier
doi:10.2996/kmj/1341401049

Mathematical Reviews number (MathSciNet)
MR2951255

Zentralblatt MATH identifier
1247.35060

Citation

Anma, Atsushi; Sakamoto, Kunimochi; Yoneda, Tohru. Unstable subsystems cause Turing instability. Kodai Math. J. 35 (2012), no. 2, 215--247. doi:10.2996/kmj/1341401049. https://projecteuclid.org/euclid.kmj/1341401049


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