Wada basin dynamics of a shallow arch oscillator with more than 20 coexisting low-period periodic attractors

In this paper, we examine a shallow arch model with viscous damping subjected to a sinusoidally varying central load. The system can possess more than 20 coexisting low-period periodic attractors for a given set of parameters. The large number of stable orbits yields a complex structure of closely interwoven basins of attraction, whose boundaries fill almost the whole state space. We describe the Wada basin boundaries and partially Wada basin boundaries by the mathematically rigorous method for some basins. The consequence is the existence of a high number of possible final states and the difficulty of predicting the finial states. Perturbations in such a system render uncertainty even the qualitative fate of a given initial state.