Resilience for stochastic systems interacting via a quasi-degenerate network

A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network, two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear lattice, noise gets amplified via a self-consistent process,...

Full description

Saved in:

Bibliographic Details
Published in:	Chaos (Woodbury, N.Y.) N.Y.), 2019-08, Vol.29 (8), p.083123-083123
Main Authors:	Nicoletti, Sara, Fanelli, Duccio, Zagli, Niccolò, Asllani, Malbor, Battistelli, Giorgio, Carletti, Timoteo, Chisci, Luigi, Innocenti, Giacomo, Livi, Roberto
Format:	Article
Language:	eng
Subjects:	Amplification Eigenvalues Embedded systems Normality Resilience Species diffusion Stochastic systems
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network, two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear lattice, noise gets amplified via a self-consistent process, which we trace back to the degenerate spectrum of the embedding support. The same phenomenon holds when the system is bound to explore a quasidegenerate network. In this case, the eigenvalues of the Laplacian operator, which governs species diffusion, accumulate over a limited portion of the complex plane. The larger the network, the more pronounced the amplification. Beyond a critical network size, a system deemed deterministically stable, hence resilient, can develop seemingly regular patterns in the concentration amount. Non-normality and quasidegenerate networks may, therefore, amplify the inherent stochasticity and so contribute to altering the perception of resilience, as quantified via conventional deterministic methods.
ISSN:	1054-1500 1089-7682