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Linear stability criteria for a reaction-diffusion equation with spatially inhomogeneous delay

Linear stability criteria for a reaction-diffusion equation with spatially inhomogeneous delay
Linear stability criteria for a reaction-diffusion equation with spatially inhomogeneous delay
Time delays play an important role in many biological and ecological systems. However, they are usually incorporated into mathematical models in a way not explicitly dependent on space, even though the delay may be modelling some environmental aspect of the system. In this paper we study a scalar reaction-diffusion equation with a spatially inhomogeneous delay, taken for simplicity in the form of a step function of the spatial coordinate. We derive the dispersion relation from which analytical results on the stability or instability of the uniform steady states can be determined. We confirm and extended these results by numerical simulations which confirm the possibility of qualitatively different types of behaviour on different parts of the spatial domain.
0268-1110
71-91
Schley, D.
3d807658-2cfd-40e6-90ba-5032f88bb54b
Gourley, S.A.
1aa9c89e-dfca-43f6-ad4d-4ecbe379094c
Schley, D.
3d807658-2cfd-40e6-90ba-5032f88bb54b
Gourley, S.A.
1aa9c89e-dfca-43f6-ad4d-4ecbe379094c

Schley, D. and Gourley, S.A. (1999) Linear stability criteria for a reaction-diffusion equation with spatially inhomogeneous delay. Dynamics and Stability of Systems, 14 (1), 71-91. (doi:10.1080/026811199282083).

Record type: Article

Abstract

Time delays play an important role in many biological and ecological systems. However, they are usually incorporated into mathematical models in a way not explicitly dependent on space, even though the delay may be modelling some environmental aspect of the system. In this paper we study a scalar reaction-diffusion equation with a spatially inhomogeneous delay, taken for simplicity in the form of a step function of the spatial coordinate. We derive the dispersion relation from which analytical results on the stability or instability of the uniform steady states can be determined. We confirm and extended these results by numerical simulations which confirm the possibility of qualitatively different types of behaviour on different parts of the spatial domain.

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Published date: 1999

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Local EPrints ID: 29281
URI: http://eprints.soton.ac.uk/id/eprint/29281
ISSN: 0268-1110
PURE UUID: 86dbbbf1-96ac-429e-b1a9-7a6012ec41d1

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Date deposited: 06 Feb 2007
Last modified: 08 Jan 2022 18:55

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Contributors

Author: D. Schley
Author: S.A. Gourley

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