Robust extremes in chaotic deterministic systems.
This paper introduces the notion of robust extremes in deterministic chaotic systems, presents initial theoretical results, and outlines associated inferential techniques. A chaotic deterministic system is said to exhibit robust extremes under a given observable when the associated statistics of extreme values depend smoothly on the system's control parameters. Robust extremes are here illustrated numerically for the flow of the Lorenz model [E. N. Lorenz, J. Atmos. Sci. 20, 130 (1963)]. Robustness of extremes is proved for one-dimensional Lorenz maps with two distinct types of observables for which conditions guaranteeing robust extremes are formulated explicitly. Two applications are shown: improving the precision of the statistical estimator for extreme value distributions and predicting future extremes in nonstationary systems. For the latter, extreme wind speeds are examined in a simple quasigeostrophic model with a robust chaotic attractor subject to nonstationary forcing.
Vitolo
Renato
R
School of Engineering, Computing and Mathematics, University of Exeter, Exeter, Devon EX4 4QF, United Kingdom. r.vitolo@exeter.ac.uk
Holland
Mark P
MP
Ferro
Christopher A T
CA
D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D012815:Signal Processing, Computer-Assisted