Master stability functions reveal diffusion-driven pattern formation in networks

Physical Review. E
Andreas BrechtelThilo Gross

Abstract

We study diffusion-driven pattern formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space. For illustration, we consider a generalized model of ecological meta-food webs. This fairly complex model describes the dispersal of many different species across a region consisting of a network of individual habitats while subject to realistic, nonlinear predator-prey interactions. In this example, the method reveals the intricate dependence of the dynamics on the spatial structure. The ability of the proposed approach to deal with this fairly complex system highlights it as a promising tool for ecology and other applications.

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Citations

Nov 6, 2018·Scientific Reports·Giulia CencettiDuccio Fanelli
Jan 11, 2020·Bulletin of Mathematical Biology·Sean M Hayes, Kurt E Anderson
Aug 24, 2019·Scientific Reports·Andreas BrechtelBarbara Drossel
Nov 3, 2020·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·Thilo GrossFanqi Zeng
Nov 29, 2020·Nature Communications·Joseph W Baron, Tobias Galla
Jan 30, 2021·Physical Review Letters·Rico BernerSerhiy Yanchuk
Sep 2, 2021·Scientific Reports·Kurt E Anderson, Ashkaan K Fahimipour
Sep 25, 2021·Ecology Letters·Christian GuillToni Klauschies

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