Visualizing the attraction of strange attractors

Abstract

We describe a simple new method that provides instructive insights into the dynamics of chaotic time-continuous systems that yield strange attractors as solutions in the phase space. In particular, we show that the norm of the vector field component that is orthogonal to the trajectory is an excellent quantity for visualizing the attraction of strange attractors, thus promoting the understanding of their formation and overall structure. Furthermore, based on the existence of zero orthogonal field strengths in planes that form low-dimensional strange attractors, we also provide an innovative explanation for the origin of chaotic behaviour. For instructive purposes, we first apply the method to a simple limit cycle attractor, and then analyse two paradigmatic mathematical models for classical time-continuous chaos. To facilitate the use of our method in graduate as well as undergraduate courses, we also provide user-friendly programs in which the presented theory is implemented.

Keywords

dinamični sistemi;kaotični sistemi;gibanje;nelinearna dinamika;atraktorji;ne zaključna dela;dynamic systems;chaotic systems;nonlinear dynamics;attractors;strange attractors;

Data

Language:	English
Year of publishing:	2005
Typology:	1.01 - Original Scientific Article
Organization:	UM PEF - Faculty of Education
UDC:	534.83:531.3
COBISS:	14505224
ISSN:	0143-0807
Views:	2270
Downloads:	82
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	dinamični sistemi;kaotični sistemi;gibanje;nelinearna dinamika;atraktorji;
URN:	URN:SI:UM:
Pages:	str. 579-587
Volume:	ǂVol. ǂ26
Issue:	ǂno. ǂ4
Chronology:	2005
DOI:	10.1088/0143-0807/26/4/003
ID:	8724266