DocumentCode
1487417
Title
Generating chaos via x|x|
Author
Tang, Kit-Sang ; Man, Kim F. ; Zhong, Guo-Qun ; Chen, Guanrong
Author_Institution
Dept. of Electron. Eng., City Univ. of Hong Kong, Kowloon, China
Volume
48
Issue
5
fYear
2001
fDate
5/1/2001 12:00:00 AM
Firstpage
636
Lastpage
641
Abstract
This paper investigates the role of the function x|x| as a chaos generator in nonautonomous systems. A Duffing-like nonautonomous oscillator is used for illustration. It is rigorously proven via the Melnikov function method that this particular quadratic function induces Smale horseshoes to the Duffing-like system. Moreover, its physical meaning as an energy function is demonstrated, which provides a critical value for the emergence of chaos. Simulations with bifurcation analysis are given for better understanding of the underlying dynamics
Keywords
bifurcation; chaos generators; nonlinear dynamical systems; oscillators; Duffing-like nonautonomous oscillator; Melnikov function method; Smale horseshoes; bifurcation analysis; chaos generator; nonautonomous systems; quadratic function; Analytical models; Bifurcation; Chaos; Chaotic communication; Circuits; Communication system control; Control systems; Oscillators; Piecewise linear techniques; Polynomials;
fLanguage
English
Journal_Title
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
Publisher
ieee
ISSN
1057-7122
Type
jour
DOI
10.1109/81.922468
Filename
922468
Link To Document