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arXiv · 1904.09844

Resilience for stochastic systems interacting via a quasi-degenerate network

Sara Nicoletti·Duccio Fanelli·Niccolò Zagli·Malbor Asllani·Giorgio Battistelli·Timoteo Carletti·Luigi Chisci·Giacomo Innocenti·Roberto Livi
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Abstract

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 quasi degenerate 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, may turn unstable, yielding seemingly regular patterns in the concentration amount. Non-normality and quasi-degenerate networks may therefore amplify the inherent stochasticity, and so contribute to altering the perception of resilience, as quantified via conventional deterministic methods.

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Sara Nicoletti, Duccio Fanelli, Niccolò Zagli, Malbor Asllani, Giorgio Battistelli, Timoteo Carletti, Luigi Chisci, Giacomo Innocenti, Roberto Livi. 2019-04-14. Resilience for stochastic systems interacting via a quasi-degenerate network. https://doi.org/10.1063/1.5099538

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