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Resilience for stochastic systems interacting via a quasi-degenerate network

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posted on 2022-10-05, 12:54 authored by Sara Nicoletti, Duccio Fanelli, Niccolò Zagli, Malbor Asllani, Giorgio Battistelli, Timoteo Carletti, Luigi Chisci, Giacomo Innocenti, Roberto Livi
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 selfconsistent process,whichwe trace back to the degenerate spectrum of the embedding support. The same phenomenon holdswhen 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.



Chaos;29, 083123


AIP Publishing




Copyright 2019 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics The following article ' Resilience for stochastic systems interacting via a quasi-degenerate network' appeared in Chaos, 2019, 29, 083123 and may be found at



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