WADA BASINS IN AN UNCONTROLLED AND CONTROLLED VIBRATION ISOLATION SYSTEM

It is an open question whether Wada basin exists in control systems. We investigate coexisting attractors and their Wada basins for a given set of parameters in an uncontrolled and controlled vibration isolation system. Wada basins are verified by the Nusse-Yorke method. All coexisting chaotic attractors can be converted into periodic attractors but the basin structure can still possess Wada property by two control methods (an external drive control and a piecewise damping control) with the appropriate control parameters. The Wada basins of controlled systems imply a particular kind of unpredictability, and we should avoid selecting such control parameters although chaotic attractors are effectively controlled.

Automated summary

We investigate the coexisting attractors and their Wada basins in a vibration isolation system under control parameters. The study shows that even though the attractors can be effectively controlled, Wada basins still exist, indicating a certain level of unpredictability in the system.