Berlin 2012 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 10: Nonlinear Dynamics, Synchronisation and Chaos

DY 10.5: Talk

Tuesday, March 27, 2012, 10:30–10:45, MA 001

Parameter-space for a dissipative Fermi-Ulam model — •Diego Fregolente Mendes de Oliveira — Institute for Multiscale Simulations - Friedrich-Alexander Universität - D-91052 - Erlangen - Germany

The parameter-space for a dissipative bouncing ball model under the effect of inelastic collisions is studied. The system is described by using a two-dimensional nonlinear area-contracting map. The introduction of dissipation destroys the mixed structure of phase space of the non-dissipative case leading to the existence of a chaotic attractor and attracting fixed points which may coexist for certain ranges of control parameters. We have computed the average velocity for the parameter space and we have made a connection with the parameter space based on the maximum Lyapunov exponent. For both cases we have found an infinite family of self-similar structures of shrimp-shape which correspond to the periodic attractors embedded in a large region which corresponds to the chaotic motion. The procedure is of broad interest and can be extended to many other different two dimensional area contracting models.