Berlin 2015 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 62: Poster - Dynamics

DY 62.2: Poster

Donnerstag, 19. März 2015, 16:00–18:00, Poster A

A prototype dynamical system with a generalized mechanical potential — •Bulcsú Sándor and Claudius Gros — Institut für Theoretische Physik, Goethe Universität, Frankfurt am Main, Germany

In dynamical systems theory, prototype systems are often used to investigate different bifurcation scenarios or certain dynamical behaviours. Systems, like the van der Pol oscillator, the Takens-Bogdanov system, or the Rössler system, are considered to be prototypical examples for the birth of limit cycles, homoclinic and period doubling bifurcations respectively, but leave little or no possibility to be reshaped for exploratory purposes while keeping their major dynamical features unchanged. Thus, one would sometimes like to design simple systems with predefined properties to understand the bifurcations of systems with higher complexity.

In this work a new class of prototype systems is proposed, which provides a mechanistic understanding for many different dynamical behaviours, including the previously mentioned bifurcations. We introduce a generalized mechanical potential which allows the local minima to be placed at arbitrary locations. Together with a velocity dependent force term one can easily control the flow through the parameters, by changing the balance between energy uptake and dissipation along the trajectory. Increasing the dimensionality of the system a whole cascade of limit cycle bifurcations is revealed, culminating in a period-doubling route to chaos.