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Internal reliability and antireliability in dynamical networks.

Tommaso Matteuzzi1, Franco Bagnoli1,2, Michele Baia1,2

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We introduce internal reliability for dynamical networks, assessing unit synchronization. Peripheral units are often antireliable, while central units tend to be reliable, depending on coupling.

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Area of Science:

  • Dynamical systems and network theory
  • Statistical physics
  • Computational neuroscience

Background:

  • Understanding the stability and behavior of interconnected units is crucial in complex systems.
  • Internal reliability defines how well replicated units in a network maintain their intended states.

Purpose of the Study:

  • To define and quantify internal reliability in finite dynamical networks.
  • To analyze reliability patterns in various coupled oscillator models, including the Kuramoto model.
  • To investigate the impact of coupling (attractive vs. repulsive) on unit reliability.

Main Methods:

  • Definition of internal reliability based on state synchronization with prototypes.
  • Quantification using the transversal Lyapunov exponent.
  • Analysis of the Kuramoto model with distributed natural frequencies.
  • Examination of other coupled oscillator models (Winfree, rotators, Stuart-Landau).

Main Results:

  • Peripheral units are antireliable and central units reliable under attractive coupling before synchronization.
  • Repulsive coupling reverses this pattern: central units are antireliable, peripheral ones reliable.
  • Large subnetworks and recurrent neural networks exhibit antireliability, while individual units are reliable.
  • Reliability in the Kuramoto model relates to phase correlations via a fluctuation-dissipation-like relation.

Conclusions:

  • Internal reliability is a quantifiable property of dynamical networks, influenced by unit properties and network topology.
  • The study reveals distinct reliability patterns in coupled oscillator systems, offering insights into network stability.
  • Findings are consistent across multiple coupled oscillator models, suggesting generalizable principles.