Abstract
In the paper, several different methods are adopted to control Lu system. With direct feedback method, Lu system can be stabilized at one equilibrium point or a limit cycle surrounding its equilibrium. With adaptive time-delayed feedback method, feedback coefficient and delay time can be adjusted adaptively to stabilize Lu system at its original unstable periodic orbit. With minimal energy method, Lu system can also be stabilized at fixed point or limit cycle. Numerical simulations show the effectiveness of our methods.
Highlights
In 1990, Ott, Grebogi and Yorke presented the OGY method to control chaos [1]
Lü system can be stabilized at equilibrium point or limit cycle around its equilibrium
We study the chaotic control of Lü system with several different methods
Summary
In 1990, Ott, Grebogi and Yorke presented the OGY method to control chaos [1]. After their pioneering work, chaotic control has become a focus in nonlinear problems and a lot of work has been done in the field [2]-[4]. Feedback methods are used to stabilize the unstable periodic orbit of chaotic systems by feeding back their states. Nonfeedback methods are adopted to change chaotic behaviors by applying perturbations to some parameters or variables. We use several different methods to control the dynamic behavior of Lü system. With adaptive time-delayed feedback method, Lü system can be stabilized at its original unstable periodic orbit.
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