Fractal Erosion of the Safe Basin in a Helmholtz Oscillator and Its Control by Linear Delayed Velocity Feedback

Fractal erosion of the safe basin in a Helmholtz oscillator system is studied. A linear delayed velocity feedback is employed to suppress the fractal erosion. The necessary basin erosion condition of the delayed feedback controlled system is obtained. The evolution of the boundary and area of the safe basin over time delay is also presented. It follows that the delayed velocity feedback can be used as an effective strategy to control fractal erosion of a safe basin.