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Extreme events in multivariate deterministic systems.

C Nicolis¹, G Nicolis

¹Institut Royal Météorologique de Belgique, Brussels, Belgium. cnicolis@oma.be

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 26, 2012

Summary

This summary is machine-generated.

Dynamical complexity in systems can mask extreme value behavior. However, specific variable combinations reveal singular behaviors, like non-differentiable distributions, in extreme value analysis.

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Area of Science:

Complex Systems
Dynamical Systems Theory
Probability Theory

Background:

Understanding extreme value behavior is crucial in analyzing complex systems.
Deterministic dynamical systems can exhibit intricate probabilistic properties.

Purpose of the Study:

To analyze the probabilistic properties of extreme values in multivariate deterministic dynamical systems.
To investigate how dynamical complexity influences extreme value distributions.

Main Methods:

Analytic evaluations of probabilistic properties.
Extensive numerical simulations on various systems (Kolmogorov-type, chaotic flows, spatially extended systems).

Main Results:

Dynamical complexity often masks extreme value effects, leading to differentiable distributions and continuous probability densities.
Singular behaviors, such as non-differentiable cumulative distributions for extremes, emerge for variable combinations probing dominant unstable modes.

Conclusions:

The interplay of stable and unstable modes in dynamical systems influences the predictability of extreme events.
Specific analyses are required to uncover hidden singular behaviors in extreme value distributions within complex systems.