Extreme amplitudes of a periodically forced Duffing oscillator

详细信息    查看全文

• 作者：A.E. Sterk ^{a.e.sterk@rug.nl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Extreme value statistics ; Dynamical systems ; Duffing oscillator
• 刊名：Indagationes Mathematicae
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：27
• 期：5
• 页码：1059-1067
• 全文大小：815 K

文摘

A novel development in the theory of deterministic dynamical systems is the application of extreme value statistics. The idea is to evaluate a scalar observable along an evolution of the system. Under appropriate conditions the large values of this time series can be interpreted as realizations of a Generalized Extreme Value (GEV) distribution. The purpose of this paper is to illustrate the methodology with a time series of amplitudes of a periodically forced Duffing oscillator. The parameters of the GEV distribution are estimated by means of a block maximum method. It will be shown that a numerical estimation of these parameters can pose serious problems due to the fractal nature of the attractor of the system.