Generating chaos via x|x|

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)22_Publication in policy or professional journal

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Original languageEnglish
Pages (from-to)636-641
Journal / PublicationIEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Issue number5
Publication statusPublished - May 2001


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.

Research Area(s)

  • Chaos, Duffing system, Piecewise quadratic function