Generating chaos via .x vertical bar x vertical bar

Citation
Ks. Tang et al., Generating chaos via .x vertical bar x vertical bar, IEEE CIRC-I, 48(5), 2001, pp. 636-641
Citations number
11
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Eletrical & Eletronics Engineeing
Journal title
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS
ISSN journal
1057-7122 → ACNP
Volume
48
Issue
5
Year of publication
2001
Pages
636 - 641
Database
ISI
SICI code
1057-7122(200105)48:5<636:GCV.VB>2.0.ZU;2-K
Abstract
This paper investigates the role of the function x \x \ as a chaos generato r 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 Du ffing-Like system. Moreover, its physical meaning as an energy function is demonstrated, which provides a critical value for the emerge of chaos. Simu lations with bifurcation analysis are given for better understanding of the underlying dynamics.