Date
2019
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 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.
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Description
peer-reviewed
Publisher
American Institute of Physics
Citation
Chaos;29, 083123
Collections
Mathematics & Statistics
MACSI - Mathematics Application Consortium for Science & Industry
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Asllani_2019_Resilience.pdf
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Keywords
network
ULRR Identifiers
https://researchrepository.ul.ie/handle/10344/8225
 https://doi.org/10.34961/4302
Funding code
Funding Information
Sustainable Development Goals
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Type
Article
Rights
https://creativecommons.org/licenses/by-nc-sa/1.0/
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