Cookies

We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.


Durham Research Online
You are in:

Turing and wave instabilities in hyperbolic reaction–diffusion systems: The role of second-order time derivatives and cross-diffusion terms on pattern formation

Ritchie, Joshua S. and Krause, Andrew L. and Van Gorder, Robert A. (2022) 'Turing and wave instabilities in hyperbolic reaction–diffusion systems: The role of second-order time derivatives and cross-diffusion terms on pattern formation.', Annals of physics. . p. 169033.

Abstract

Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct features in terms of propagation speed and novel instabilities not present in classical two-species reaction-diffusion systems. We explore the onset of diffusive instabilities and resulting pattern formation for such systems. Starting with a rather general formulation of the problem, we obtain necessary and sufficient conditions for the Turing and wave instabilities in such systems, thereby classifying parameter spaces for which these diffusive instabilities occur. We find that the additional temporal terms do not strongly modify the Turing patterns which form or parameters which admit them, but only their regions of existence. This is in contrast to the case of additional space derivatives, where past work has shown that resulting patterned structures are sensitive to second-order cross-diffusion and first-order advection. We also show that additional temporal terms are necessary for the emergence of spatiotemporal patterns under the wave instability. We find that such wave instabilities exist for parameters which are mutually exclusive to those parameters leading to stationary Turing patterns. This implies that wave instabilities may occur in cases where the activator diffuses faster than the inhibitor, leading to routes to spatial symmetry breaking in reaction-diffusion systems which are distinct from the well studied Turing case.

Item Type:Article
Full text:Publisher-imposed embargo until 21 July 2023.
(AM) Accepted Manuscript
File format - PDF
(8949Kb)
Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.aop.2022.169033
Publisher statement:© 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:12 July 2022
Date deposited:01 August 2022
Date of first online publication:21 July 2022
Date first made open access:21 July 2023

Save or Share this output

Export:
Export
Look up in GoogleScholar