TY - JOUR
T1 - Resilience for stochastic systems interacting via a quasi-degenerate network
AU - Nicoletti, Sara
AU - Fanelli, Duccio
AU - Zagli, Niccolò
AU - Asllani, Malbor
AU - Battistelli, Giorgio
AU - Carletti, Timoteo
AU - Chisci, Luigi
AU - Innocenti, Giacomo
AU - Livi, Roberto
PY - 2019/8/1
Y1 - 2019/8/1
N2 - 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.
AB - 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.
KW - Resilience
KW - stochastic dynamics
KW - Reaction-diffusion systems
KW - network
UR - http://www.scopus.com/inward/record.url?scp=85071336566&partnerID=8YFLogxK
U2 - 10.1063/1.5099538
DO - 10.1063/1.5099538
M3 - Article
SN - 1054-1500
VL - 29
JO - Chaos: an interdisciplinary journal of nonlinear science
JF - Chaos: an interdisciplinary journal of nonlinear science
IS - 8
M1 - 083123
ER -