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Bifurcation and Chaos in the Duffing Oscillator with a PID Controller (1997)

Cui, Fangsen ; Chew, C. H. ; Xu, Jianxue ; [et al.]

Springer

Nonlinear dynamics 12 (1997), S. 251-262

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ISSN: 1573-269X

Keywords: Bifurcation ; chaos ; Duffingoscillator ; fractal basin boundary ; PIDcontroller

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We discuss in this paper the bifurcation, stability and chaos of the non-linear Duffing oscillator with a PID controller. Hopf bifurcation can occur and we show that there is a global stable fixed point. The PID controller works well in some fields of the parameter space, but in other fields of the parameter space, or if the reference input is not equal to zero, chaos is common for hard spring type system and so is fractal basin boundary for soft spring system. The Melnikov method is used to obtain the criterion of fractal basin boundary.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1008204332684

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