Title: Chasing patterns: diffusion-driven instabilities in networked and high-order systems

Speaker: Riccardo Muolo (Université de Namur)
October 10 from 3:30 p.m. to 4:30 p.m.
Local: Sala B106-a – Bloco B – CT – Instituto de Matemática – UFRJ

Abstract: Many natural and artificial systems exhibit collective behaviors, which show in the form of spatio-temporal patterns. This has triggered the interests of scholars, who have proposed several theories to account for such diversity. One of the most popular mechanisms of pattern formation is due to Alan Turing, who showed that diffusion can disrupt a homogeneous stable state, triggering an instability [1]. The original theory has been conceived in the framework of reaction-diffusion PDEs, but it has been recently extended on networked systems [2]. Moreover, it has been shown that a Turing-like mechanism occurs in the framework of synchronized coupled oscillators, as diffusion can lead to a loss of synchronization [3]. 
In this seminar I will present an overview of Turing theory in networked systems, showing that the Turing framework is indeed not too far from that of coupled chaotic oscillators [4]. I will then focus the attention on two results we have recently obtained. The first one, about the study of reaction-diffusion systems on top of non-normal networks, i.e., networks whose adjacency matrix is non-normal [5]. Such topology makes the system more sensible to perturbation, leading to a loss of stability even when a linear stability analysis predicts otherwise [6, 7]. Finally, I will briefly introduce high-order structures, i.e., hypergraphs and simplicial complexes, and show a recent extension of Turing theory on such topologies [8].

References
[1] A M Turing. The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B, 237:37, 1952.
[2] Hiroya Nakao and Alexander S Mikhailov. Turing patterns in network-organized activator-inhibitor systems. Nature Physics, 6:544, 2010.
[3] J Challenger, D Fanelli, and R Burioni. Turing-like instabilities from a limit cycle. Phys. Rev. E, 92:022818, 2015.
[4] Louis M Pecora and Thomas L Carroll. Master stability functions for synchronized coupled systems. Physical Review Letters, 80(10):2109, 1998.
[5] Malbor Asllani, Renaud Lambiotte, and Timoteo Carletti. Structure and dynamics of non-normal networks. Sci. Adv., 4:Eaau9403, 2018.
[6] Riccardo Muolo, Malbor Asllani, Duccio Fanelli, Ph K Maini, and Timoteo Carletti. Patterns of non-normality in networked systems. Journal of Theoretical Biology, 480:81, 2019.
[7] Riccardo Muolo, Timoteo Carletti, James P Gleeson, and Malbor Asllani. Synchronization dynamics in non-normal networks: the trade-off for optimality. Entropy, 23:36, 2021.
[8] Riccardo Muolo, Luca Gallo, Vito Latora, Mattia Frasca, and Timoteo Carletti. Turing patterns in systems with high-order interaction. arXiv preprint arXiv:2207.03985, 2022.

All the talks are held in English.

More complete information about the seminars will be available at Here.

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