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Area of Science:

  • Network science
  • Complex systems
  • Dynamical processes

Background:

  • Empirical networks across various disciplines reveal ubiquitous strong non-normality.
  • Non-normal network dynamics can lead to transient amplification of disturbances in stable systems.
  • Eigenvalues in non-normal systems are sensitive to noise, diminishing their physical interpretability.

Purpose of the Study:

  • To investigate the prevalence and implications of non-normality in empirical networks.
  • To identify network structural properties associated with non-normality.
  • To propose models for generating networks with tunable non-normality and explore its application in ecosystem stability.

Main Methods:

  • Analysis of a diverse collection of empirical networks.
  • Identification of structural network properties linked to non-normality.
  • Development of simple models for generating networks with controlled non-normality levels.

Main Results:

  • Strong non-normality is a widespread characteristic of empirical networks.
  • Non-normal dynamics can cause significant amplification of initial disturbances, even in linearly stable systems.
  • Network structure influences non-normality; tunable models were developed.

Conclusions:

  • Non-normality significantly affects the behavior of dynamical processes on networks.
  • Metrics capturing non-normality are valuable for assessing the stability of complex systems, such as ecosystems.
  • Understanding non-normality is crucial for accurate network analysis and prediction.