Generating chaos via x|x|

K. S. Tang; K. F. Man; G. Q. Zhong; G. Chen

doi:10.1109/81.922468

Generating chaos via x|x|

K. S. Tang
, K. F. Man
, G. Q. Zhong
, G. Chen

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 22 - Publication in policy or professional journal

95 Citations (Scopus)

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 emerge of chaos. Simulations with bifurcation analysis are given for better understanding of the underlying dynamics.

Original language	English
Pages (from-to)	636-641
Journal	IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume	48
Issue number	5
DOIs	https://doi.org/10.1109/81.922468
Publication status	Published - May 2001

Research Keywords

Chaos
Duffing system
Piecewise quadratic function

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AB - 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 emerge of chaos. Simulations with bifurcation analysis are given for better understanding of the underlying dynamics.

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KW - Duffing system

KW - Piecewise quadratic function

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JF - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

IS - 5

ER -

Generating chaos via x|x|

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