UNSPECIFIED (1995) TURING BIFURCATIONS WITH A TEMPORALLY VARYING DIFFUSION-COEFFICIENT. JOURNAL OF MATHEMATICAL BIOLOGY, 33 (3). pp. 295-308. ISSN 0303-6812

Full text not available from this repository.

Abstract

This paper is concerned with the possibility of Turing bifurcations in a reaction-diffusion system in which the diffusion coefficient of one species varies periodically in time. This problem was introduced and investigated numerically by Timm and Okubo (J. Math. Biol. 30, 307, 1992) in the context of predator-prey interactions in plankton populations. Here, I consider the simple case in which the temporal variation in diffusivity has a square-tooth form, alternating between two constant values, with a period that is long compared with the time scale of the kinetics. The analysis is valid for any set of reaction kinetics. I derive explicit expressions for the Floquet multipliers that determine the stability of the steady state, and thereby obtain the conditions for diffusion driven instability to occur. These conditions imply that, depending on the kinetics, the homogeneous equilibrium may be either more or less stable than when the diffusion coefficient is a constant equal to the mean of the variable diffusivity. I go on to consider the form of the solution when diffusion driven instability does occur, and I use perturbation theory to determine the effect of a small temporal variation in the diffusion coefficient on the spatial wavelength of the pattern that results from diffusion driven instability.

Item Type:	Journal Article
Subjects:	Q Science > QH Natural history > QH301 Biology
Journal or Publication Title:	JOURNAL OF MATHEMATICAL BIOLOGY
Publisher:	SPRINGER VERLAG
ISSN:	0303-6812
Date:	January 1995
Volume:	33
Number:	3
Number of Pages:	14
Page Range:	pp. 295-308
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/20045

Data sourced from Thomson Reuters' Web of Knowledge

Request changes to a record

Actions (login required)

View Item