Topological resilience in non-normal networked systems

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Abstract

The network of interactions in complex systems strongly influences their resilience and the system capability to resist external perturbations or structural damages and to promptly recover thereafter. The phenomenon manifests itself in different domains, e.g., parasitic species invasion in ecosystems or cascade failures in human-made networks. Understanding the topological features of the networks that affect the resilience phenomenon remains a challenging goal for the design of robust complex systems. We hereby introduce the concept of non-normal networks, namely networks whose adjacency matrices are non-normal, propose a generating model, and show that such a feature can drastically change the global dynamics through an amplification of the system response to exogenous disturbances and eventually impact the system resilience. This early stage transient period can induce the formation of inhomogeneous patterns, even in systems involving a single diffusing agent, providing thus a new kind of dynamical instability complementary to the Turing one. We provide, first, an illustrative application of this result to ecology by proposing a mechanism to mute the Allee effect and, second, we propose a model of virus spreading in a population of commuters moving using a non-normal transport network, the London Tube.
Original languageEnglish
Article number042302
Pages (from-to)1-12
Number of pages12
JournalPhys. Rev. E
Volume97
Issue number4
DOIs
Publication statusPublished - 4 Apr 2018

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resilience
complex systems
ecology
ecosystems
viruses
cascades
disturbances
tubes
damage
perturbation
matrices

Keywords

  • Dynamical systems
  • complex network
  • resilience
  • non-normal networks
  • Reaction-diffusion model
  • Allee effect
  • Turing patterns

Cite this

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title = "Topological resilience in non-normal networked systems",
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Topological resilience in non-normal networked systems. / Asllani, Malbor; Carletti, Timoteo.

In: Phys. Rev. E , Vol. 97, No. 4, 042302, 04.04.2018, p. 1-12.

Research output: Contribution to journalArticle

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AB - The network of interactions in complex systems strongly influences their resilience and the system capability to resist external perturbations or structural damages and to promptly recover thereafter. The phenomenon manifests itself in different domains, e.g., parasitic species invasion in ecosystems or cascade failures in human-made networks. Understanding the topological features of the networks that affect the resilience phenomenon remains a challenging goal for the design of robust complex systems. We hereby introduce the concept of non-normal networks, namely networks whose adjacency matrices are non-normal, propose a generating model, and show that such a feature can drastically change the global dynamics through an amplification of the system response to exogenous disturbances and eventually impact the system resilience. This early stage transient period can induce the formation of inhomogeneous patterns, even in systems involving a single diffusing agent, providing thus a new kind of dynamical instability complementary to the Turing one. We provide, first, an illustrative application of this result to ecology by proposing a mechanism to mute the Allee effect and, second, we propose a model of virus spreading in a population of commuters moving using a non-normal transport network, the London Tube.

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