Resilience for stochastic systems interacting via a quasi-degenerate network

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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Cited by in corpus (6)

• Turing patterns on discrete topologies: from networks to higher-order structures
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• Broken detailed balance and entropy production in directed networks
• Non-normality and non-monotonic dynamics in complex reaction networks
• Persistence of chimera states and the challenge for synchronization in real-world networks
• Hierarchical route to the emergence of leader nodes in real-world networks