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DTSTART;TZID=Europe/Paris:20191017T130000
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DTSTAMP:20260429T202647
CREATED:20190911T091448Z
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UID:593-1571317200-1571320800@www.naxys.be
SUMMARY:Riccardo Muolo (UNamur)
DESCRIPTION:Title: Effects of Non-normality on Turing Instability \nAbstract: Turing mechanism describes the emergence of spatial patterns in a reaction-diffusion system of two or more species: when certain conditions are matched\, a perturbation starting from a homogeneous stable state guides the system towards a nonhomogeneous one\, the celebrated Turing patterns\, following a diffusion-driven instability [1]. The classical linear stability analysis that describes such phenomenon is based on the spectra of involved the operators. However\, such analysis may fail when the involved linear operators are non-normal\, due to a transient growth [2]. Such effect is even stronger when the system is studied on a non-normal network\, i.e.\, a network whose adjacency matrix is non-normal [3]. In a recently published work [4] we have made use of such theoretical background to extend the original theory by obtaining non-normality patterns when Turing contitions are not satisfied.\nIn this seminar I will go through the main steps of this itinerary\, from classical Turing Instability to patterns of non-normality. Firstly\, I will present qualitatively the idea of Turing\, then\, after having introduced the notion of network\, I will talk about processes of diffusion on discrete support\, I will explain a recent extention of Turing Theory on symmetric network [5] and how an asymmetric topology can affect the mechanism of pattern formation [6]. Before moving to the last part\, I will introduce the concept of non-normality and its effects on the dynamics [7]. Finally\, I will present our extension of Turing Theory on non-normal networks [4] and discuss some open problems and possible future developments. \nReferences\n[1] Turing\, A.M.\, 1952. The chemical basis of morphogenesis. Phil. Trans. R. Soc. B 237\, 37–72;\n[2] Trefethen\, L.N.\, Embree\, M.\, 2005. Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press\, Princeton\, NJ;\n[3] Asllani\, M.\, Lambiotte\, R.\, Carletti\, T.\, 2018. Structure and dynamics of non-normal networks\, Sci. Adv. 4\, 1–8. Eaau9403;\n[4] Muolo\, R.\, Asllani\, M.\, Fanelli\, D.\, Maini\, P.K.\, Carletti\, T.\, 2019. Patterns of non-normality in networked systems. Journal of Theoretical Biology 480 81–91;\n[5] Nakao\, H.\, Mikhailov\, A.S.\, 2010. Turing patterns in network-organized activator-inhibitor systems. Nat. Phys. 6\, 544;\n[6] Asllani\, M.\, Challenger\, J.D.\, Pavone\, F.S.\, Sacconi\, L.\, Fanelli\, D.\, 2014. The theory of pattern formation on directed networks. Nat. Comm. 5\, 4517;\n[7] Asllani\, M.\, Carletti\, T.\, 2018. Topological resilience in non-normal networked systems. Phys. Rev. E 97\, 042302.
URL:https://www.naxys.be/event/riccardo-muolo/
LOCATION:E25
CATEGORIES:NAXYS Seminar
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