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Lyapunov exponents for temporal networks.

Annalisa Caligiuri1, Victor M Eguíluz1,2,3, Leonardo Di Gaetano4

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We introduce a new method to measure the dynamical instability of temporal networks by estimating their network maximum Lyapunov exponent (nMLE). This approach quantifies sensitive dependence on initial conditions in network dynamics.

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Area of Science:

  • Complex Systems Science
  • Network Science
  • Nonlinear Dynamics

Background:

  • Temporal networks represent dynamic systems where interactions evolve over time.
  • Understanding the stability and predictability of these evolving networks is crucial.
  • Existing methods struggle to capture the inherent instability in complex temporal network dynamics.

Purpose of the Study:

  • To introduce the concept of dynamical instability for temporal networks.
  • To develop a method for estimating the network maximum Lyapunov exponent (nMLE) from network trajectories.
  • To quantify sensitive dependence on initial conditions in temporal network evolution.

Main Methods:

  • Interpreting temporal networks as trajectories of latent graph dynamical systems.
  • Extending nonlinear time-series analysis algorithms to network data.
  • Directly estimating the nMLE from a single observed network trajectory.

Main Results:

  • Successfully constructed a measure to estimate the nMLE of temporal networks.
  • Demonstrated the quantification of sensitive dependence on initial conditions for network dynamics.
  • Validated the method on synthetic generative network models exhibiting low- and high-dimensional chaos.

Conclusions:

  • The proposed method provides a novel way to assess the predictability and stability of temporal networks.
  • This framework allows for the analysis of chaotic dynamics within evolving network structures.
  • Potential applications span various fields analyzing dynamic systems and their emergent behaviors.