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Control of Erosion of Safe Basins in a Helmholtz Oscillator via Delayed Velocity Feedbacks

Shang Hui-lin(School of Mechanical and Automation Engineering;Shanghai Institute of Technology;Shanghai;20035;China)

  A linear delayed velocity feedback control is used to control fractal erosion of safe basins in a Helmholtz oscillator system.The condition of fractal erosion of the basin boundary of the delayed feedback controlled system and on the basis the threshold of the excitation of the fractal erosion is obtained.Then considering time delay as a variable parameter and employing the 4th Runge-Kutta and the point-to-point mapping methods,evolutions of safe basins with time delay are presented.Our numerical simulations show that the increasing of time delay can enhance the threshold of the fractal erosion and reduce the erosion of safe basin effectively under a weak feedback gain.All the results have an implication that the delayed velocity feedback can be used as a good strategy to control the erosion of safe basins.……