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- Title
Turing Patterns in Networks.
- Authors
Ortiz Durán, Elizabeth Alejandra; Parra Verde, Daniel Ivan
- Abstract
The first pattern formation model was proposed by the mathematician Alan M. Turing. This model consists of a system of reaction-diffusion equations that produces stationary patterns by means of the so-called "Turing instability." In this paper, we found the conditions that the network and the parameters need to fulfill in order to achieve the Turing instability in a particular reaction-diffusion system called the Mimura-Murray model on different network topologies, including some simulations on an innovative kind of network, based on the Wolfram model, that evolves over time, generating interesting topologies that exhibit lattice-like topology. In addition, the equations are solved and simulated in Wolfram Language, and some examples of applications in biology and sociology are presented.
- Subjects
TURING, Alan Mathison, 1912-1954; REACTION-diffusion equations; ELECTRIC network topology; TOPOLOGY; MATHEMATICIANS
- Publication
Complex Systems, 2023, Vol 32, Issue 3, p253
- ISSN
0891-2513
- Publication type
Article
- DOI
10.25088/ComplexSystems.32.3.253