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Title: Bifurcation and Chaos in the Duffing Oscillator with a PID Controller
Authors: Cui, F.
Chew, C.H. 
Xu, J.
Cai, Y.
Keywords: Bifurcation
Duffing oscillator
Fractal basin boundary
PID controller
Issue Date: 1997
Citation: Cui, F.,Chew, C.H.,Xu, J.,Cai, Y. (1997). Bifurcation and Chaos in the Duffing Oscillator with a PID Controller. Nonlinear Dynamics 12 (3) : 251-262. ScholarBank@NUS Repository.
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.
Source Title: Nonlinear Dynamics
ISSN: 0924090X
Appears in Collections:Staff Publications

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