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
fDate :
5/1/2001 12:00:00 AM
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;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
