Journal
JOURNAL OF THE ROYAL SOCIETY INTERFACE
Volume 19, Issue 188, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsif.2021.0739
Keywords
reaction-diffusion systems; pattern formation; optimal control; network theory; instability analysis; discrete systems
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This article presents a solution to the problem of controlling Turing patterns in networks, utilizing an analytical framework and numerical algorithm. The authors demonstrate the effectiveness of their method and discuss factors that impact its performance. They also pave the way for multidisciplinary applications of their framework beyond reaction-diffusion models.
Patterns in nature are fascinating both aesthetically and scientifically. Alan Turing's celebrated reaction-diffusion model of pattern formation from the 1950s has been extended to an astounding diversity of applications: from cancer medicine, via nanoparticle fabrication, to computer architecture. Recently, several authors have studied pattern formation in underlying networks, but thus far, controlling a reaction-diffusion system in a network to obtain a particular pattern has remained elusive. We present a solution to this problem in the form of an analytical framework and numerical algorithm for optimal control of Turing patterns in networks. We demonstrate our method's effectiveness and discuss factors that affect its performance. We also pave the way for multidisciplinary applications of our framework beyond reaction-diffusion models.
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