Non-Archimedean Models of Morphogenesis

2020/09/30 by Zúñiga-Galindo, W. A. · 1 citation
#47S10. Secondary: 92C42 #Analysis of PDEs (math.AP) #FOS: Biological sciences #FOS: Mathematics #Populations and Evolution (q-bio.PE) #Primary: 35K57

paper · doi:10.48550/arxiv.2009.14752

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.

Cited by

• A p-adic Reaction--Diffusion Model of Branching Coral Growth and Calcification Dynamics

Related

• Reaction-diffusion Equations on Complex Networks and Turing Patterns, via p-Adic Analysis
• Turing Patterns in a Morphogenetic Model with Single Regulatory Function
• Formation and Persistence of Spatiotemporal Turing Patterns
• Turing patterns in systems with high-order interactions
• Turing pattern or system heterogeneity? A numerical continuation approach to assessing the role of Turing instabilities in heterogeneous reaction-diffusion systems