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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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
Issue number8
Publication statusPublished - 1 Aug 2019


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


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