Volume 80, Number 4, November 2007
Article Number 40003
Number of page(s) 6
Section General
Published online 16 October 2007
EPL, 80 (2007) 40003
DOI: 10.1209/0295-5075/80/40003

Return time statistics of extreme events in deterministic dynamical systems

C. Nicolis1 and S. C. Nicolis2

1  Institut Royal Météorologique de Belgique - 3, Avenue Circulaire, 1180 Brussels, Belgium
2  Department of Zoology, University of Oxford - South Parks Road, OX1 3PS Oxford, UK

received 21 May 2007; accepted in final form 14 September 2007; published November 2007
published online 16 October 2007

It is shown that deterministic dynamics leaves a clearcut signature on the statistical properties of the return time of extreme events, giving rise to properties that are not accounted for by the classical statistical approach. Analytical expressions are derived, compared to those of classical statistical theory and applied to generic examples of dynamical systems giving rise to quasi-periodic, strongly chaotic and intermittent chaotic behaviors.

05.45.-a - Nonlinear dynamics and chaos.
02.50.-r - Probability theory, stochastic processes, and statistics.
05.20.-y - Classical statistical mechanics.

© Europhysics Letters Association 2007