Bifurcation control and chaos in a linear impulsive system
Jiang Gui-Rong(蒋贵荣)a)b),Xu Bu-Gong(胥布工) c), and Yang Qi-Gui (杨启贵)a)†
a School of Mathematical Sciences, South China University of Technology, Guangzhou 510641, China; b School of Mathematical Sciences, South China University of Technology, Guangzhou 510641, China; c College of Automation Science and Engineering, South China University of Technology, Guangzhou 510641, China
Abstract Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto's definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.
Received: 07 November 2008
Revised: 26 June 2009
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China (Grant Nos 10871074 and
10572011) and the Natural Science Foundation of Guangxi Province,
China (Grant No 0832244).
Cite this article:
Jiang Gui-Rong(蒋贵荣),Xu Bu-Gong(胥布工), and Yang Qi-Gui (杨启贵) Bifurcation control and chaos in a linear impulsive system 2009 Chin. Phys. B 18 5235
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