Basins of Attraction and Transient Chaos in a Gear-Rattling Model

The authors numerically investigate basins of attraction of coexisting periodic and chaotic attrac tors in a gear-rattling impact model. These attractors are strongly dependent on small changes of the initial conditions. Gradually varying a control parameter, the size of these basins of attraction is modified by global bifurcations of their boundaries. Moreover, the topology of these basins is also modified by appearance or disappearance of coexisting attractors. Furthermore, for the considered control parameter range, the frac tal basin boundaries are so interleaved that trajectories are practically unpredictable in some regions of phase space. The authors also examine an example of a crisis on which a chaotic attractor is converted into a chaotic transient that goes to a periodic attractor. For this crisis, the authors show the evolution of transient lifetime dependence of the initial conditions as the control parameter is varied.