Diego, XavierMarcon, Luciano, 1983-Müller, PatrickSharpe, James2019-12-032019-12-032018Diego X, Marcon L, Müller P, Sharpe J. Key features of turing systems are determined purely by network topology. Phys Rev X. 2018;8(2):021071. DOI: 10.1103/PhysRevX.8.0210712160-3308http://hdl.handle.net/10230/43059Turing’s theory of pattern formation is a universal model for self-organization, applicable to many systems in physics, chemistry, and biology. Essential properties of a Turing system, such as the conditions for the existence of patterns and the mechanisms of pattern selection, are well understood in small networks. However, a general set of rules explaining how network topology determines fundamental system properties and constraints has not been found. Here we provide a first general theory of Turing network topology, which proves why three key features of a Turing system are directly determined by the topology: the type of restrictions that apply to the diffusion rates, the robustness of the system, and the phase relations of the molecular species.application/pdfeng© Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license (https://creativecommons.org/licenses/by/4.0/). Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.info:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevX.8.021071Biological physics complex systemsNonlinear dynamicsinfo:eu-repo/semantics/openAccess