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Routes to extreme events in dynamical systems: Dynamical and statistical characteristics.

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Extreme events in dynamical systems suddenly emerge at critical parameter values. These rare, large amplitude events, often driven by instabilities, are characterized and analyzed in exemplary systems.

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Area of Science:

  • Complex Systems Science
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Dynamical systems often exhibit intermittent large amplitude events.
  • These events arise from instabilities like interior crisis, Pomeau-Manneville intermittency, and quasiperiodic motion breakdown.
  • Extreme events are defined as those exceeding a statistically significant threshold.

Purpose of the Study:

  • To characterize extreme events in dynamical systems.
  • To illustrate the mechanisms leading to extreme events using exemplary systems.
  • To analyze the dynamical and statistical properties of these non-trivial events.

Main Methods:

  • Analysis of temporal evolution of state variables in dynamical systems.
  • Identification of critical parameter values triggering intermittent events.
  • Characterization of events exceeding a statistically defined significant height.
  • Illustration using single and coupled system models.

Main Results:

  • Demonstration of how instabilities originate extreme events.
  • Observation of extreme events manifesting as non-trivial dynamical behaviors.
  • Characterization of the dynamical and statistical properties of these events.

Conclusions:

  • Instabilities play a crucial role in the sudden onset of extreme events in dynamical systems.
  • Extreme events, though rare, are predictable features of certain dynamical systems.
  • Understanding these events is vital for analyzing complex system behaviors.