Oscillatory and phase dimensions of solutions of some second-order differential equations

被引：14
|
作者：
Pasic, Mervan [1 ]
Zubrinic, Darko [1 ]
Zupanovic, Vesna [1 ]
机构：
[1] Univ Zagreb, Dept Math, FER, Zagreb 10000, Croatia
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2009年 / 133卷 / 08期
关键词：
Nonlinear differential equation; Nonlinear oscillations; Box dimension; Chirp; Spiral; Lienard equation; Weakly damped oscillator; SPIRAL TRAJECTORIES; FRACTAL ANALYSIS;
D O I：
10.1016/j.bulsci.2008.03.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In order to measure fractal oscillatority of solutions at t = infinity, we define oscillatory and phase dimensions of solutions of a class of second-order nonlinear differential equations. The relation between these two dimensions is found using formulas for box dimension of chirps and nonrectifiable spirals. Applications include the Lienard equation and weakly damped oscillators. (C) 2008 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：859 / 874
页数：16
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