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Rotating waves in scalar systems with Neumann boundary conditions

Rotating waves in scalar systems with Neumann boundary conditions
Rotating waves in scalar systems with Neumann boundary conditions
Rotating and spiral waves occur in a variety of biological and chemical systems, such as the Belousov-Zhabotinskii reaction. Existence of such solutions is well known for a number of different coupled reaction-diffusion models, although analytical results are usually difficult to obtain. Traditionally, rotating and spiral waves have been thought to arise only in coupled systems of equations, although recent work has shown that such solutions are also possible in scalar equations if suitable boundary conditions are imposed. Such spiral or rotating boundaries are not, however, physically realistic. In this paper, we consider a class of scalar equations incorporating a discrete delay. We find that the time delay can bring about rotating wave solutions (through a Hopf bifurcation from a nontrivial spatially uniform equilibrium) in equations with homogeneous Neumann boundary conditions.
reaction-diffusion, rotating waves, time-delay, hopf bifurcation
0895-7177
767-778
Schley, D.
3d807658-2cfd-40e6-90ba-5032f88bb54b
Schley, D.
3d807658-2cfd-40e6-90ba-5032f88bb54b

Schley, D. (2003) Rotating waves in scalar systems with Neumann boundary conditions. Mathematical and Computer Modelling, 37 (7-8), 767-778. (doi:10.1016/S0895-7177(03)00084-0).

Record type: Article

Abstract

Rotating and spiral waves occur in a variety of biological and chemical systems, such as the Belousov-Zhabotinskii reaction. Existence of such solutions is well known for a number of different coupled reaction-diffusion models, although analytical results are usually difficult to obtain. Traditionally, rotating and spiral waves have been thought to arise only in coupled systems of equations, although recent work has shown that such solutions are also possible in scalar equations if suitable boundary conditions are imposed. Such spiral or rotating boundaries are not, however, physically realistic. In this paper, we consider a class of scalar equations incorporating a discrete delay. We find that the time delay can bring about rotating wave solutions (through a Hopf bifurcation from a nontrivial spatially uniform equilibrium) in equations with homogeneous Neumann boundary conditions.

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More information

Published date: 2003
Keywords: reaction-diffusion, rotating waves, time-delay, hopf bifurcation

Identifiers

Local EPrints ID: 29287
URI: http://eprints.soton.ac.uk/id/eprint/29287
ISSN: 0895-7177
PURE UUID: 67094457-22df-48f8-b086-73db41c9c1fb

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Date deposited: 12 May 2006
Last modified: 27 Apr 2022 12:17

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Author: D. Schley

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