Calculation of Lyapunov exponents in systems with impacts

被引:87
作者
de Souza, SLT [1 ]
Caldas, IL [1 ]
机构
[1] Univ Sao Paulo, Inst Fis, BR-05315970 Sao Paulo, SP, Brazil
基金
巴西圣保罗研究基金会;
关键词
D O I
10.1016/S0960-0779(03)00130-9
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We apply a model based algorithm for the calculation of the spectrum of the Lyapunov exponents of attractors of mechanical systems with impacts. For that, we introduce the transcendental maps that describe solutions of integrable differential equations, between impacts, supplemented by transition conditions at the instants of impacts. We apply this procedure to an impact oscillator and to an impact-pair system (with periodic and chaotic driving). In order to show the method precision, for large parameters range, we calculate Lyapunov exponents to classify attractors observed in bifurcation diagrams. In addition, we characterize the system dynamics by the largest Lyapunov exponent diagram in the parameter space. (C) 2003 Elsevier Ltd. All rights reserved.
引用
收藏
页码:569 / 579
页数:11
相关论文
共 19 条
[1]  
Alligood K.T., 1997, CHAOS INTRO DYNAMICA, DOI 10.1063/1.882006
[2]  
[Anonymous], 1988, DETERMINISTIC CHAOS
[3]  
[Anonymous], 1993, CHAOS DYNAMICAL SYST
[4]   Analysis of an impact damper of vibrations [J].
Blazejczyk-Okolewska, B .
CHAOS SOLITONS & FRACTALS, 2001, 12 (11) :1983-1988
[5]   Co-existing attractors of impact oscillator [J].
Blazejczyk-Okolewska, B ;
Kapitaniak, T .
CHAOS SOLITONS & FRACTALS, 1998, 9 (08) :1439-1443
[6]   Practical riddling in mechanical systems [J].
Blazejczyk-Okolewska, B ;
Brindley, J ;
Kapitaniak, T .
CHAOS SOLITONS & FRACTALS, 2000, 11 (15) :2511-2514
[7]   Basins of attraction and transient chaos in a gear-rattling model [J].
de Souza, SLT ;
Caldas, IL .
JOURNAL OF VIBRATION AND CONTROL, 2001, 7 (06) :849-862
[8]   ERGODIC-THEORY OF CHAOS AND STRANGE ATTRACTORS [J].
ECKMANN, JP ;
RUELLE, D .
REVIEWS OF MODERN PHYSICS, 1985, 57 (03) :617-656
[9]   Numerical computation of Lyapunov exponents in discontinuous maps implicitly defined [J].
Galvanetto, U .
COMPUTER PHYSICS COMMUNICATIONS, 2000, 131 (1-2) :1-9
[10]  
Guckenheimer J., 1983, NONLINEAR OSCILLATIO, V42