Non-Archimedean Models of Morphogenesis

Abstract

We study a p-adic reaction-diffusion system and the associated Turing patterns. We establish an instability criteria and show that the Turing patterns are not classical patterns consisting of alternating domains. Instead of this, a Turing pattern consists of several domains (clusters), each of them supporting a different pattern but with the same parameter values. This type of patterns are typically produced by reaction-diffusion equations on large networks.

Final version to appear in Advances in Non-Archimedean Analysis and Applications. The p-adic Methodology in STEAM-H. Editors: Zúñiga-Galindo, W., Toni, Bourama (Eds.) Springer Nature, ISBN: 978-3-030-81975-0, 2021. arXiv admin note: substantial text overlap with arXiv:1905.02128