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 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.

Original languageEnglish
Article number083123
Number of pages11
JournalChaos: an interdisciplinary journal of nonlinear science
Volume29
Issue number8
DOIs
Publication statusPublished - 1 Aug 2019

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resilience
Stochastic systems
Resilience
Stochastic Systems
Amplification
species diffusion
Non-normality
Reaction-diffusion Model
Stochasticity
Accumulate
Argand diagram
embedding
Patch
Stochastic Model
eigenvalues
Trace
Eigenvalue
operators
Unit
Interaction

Keywords

  • Resilience
  • stochastic dynamics
  • Reaction-diffusion systems
  • network

Cite this

Nicoletti, Sara ; Fanelli, Duccio ; Zagli, Niccolò ; Asllani, Malbor ; Battistelli, Giorgio ; Carletti, Timoteo ; Chisci, Luigi ; Innocenti, Giacomo ; Livi, Roberto. / Resilience for stochastic systems interacting via a quasi-degenerate network. In: Chaos: an interdisciplinary journal of nonlinear science. 2019 ; Vol. 29, No. 8.
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Resilience for stochastic systems interacting via a quasi-degenerate network. / Nicoletti, Sara; Fanelli, Duccio; Zagli, Niccolò; Asllani, Malbor; Battistelli, Giorgio; Carletti, Timoteo; Chisci, Luigi; Innocenti, Giacomo; Livi, Roberto.

In: Chaos: an interdisciplinary journal of nonlinear science, Vol. 29, No. 8, 083123, 01.08.2019.

Research output: Contribution to journalArticle

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