Basins of attraction and transient chaos in a gear-rattling model

The authors numerically investigate basins of attraction of coexisting peri odic and chaotic attractors in a gear-rattling impact model. These attracto rs are strongly dependent on small changes of the initial conditions. Gradu ally varying a control parameter, the size of these basins of attraction is modified by global bifurcations of their boundaries. Moreover, the topolog y of these basins is also modified by appearance or disappearance of coexis ting attractors. Furthermore, for the considered control parameter range, t he fractal basin boundaries are so interleaved that trajectories are practi cally unpredictable in some regions of phase space. The authors also examin e an example of a crisis on which a chaotic attractor is converted into a c haotic transient that goes to a periodic attractor. For this crisis, the au thors show the evolution of transient lifetime dependence of the initial co nditions as the control parameter is varied.