Seminars of the Focus Area Complex Systems

Prof. Dr. C. Beta, Prof. Dr. K. Dethloff, Prof. Dr. R. Engbert, Prof. Dr. M. Holschneider, Prof. Dr. W. Huisinga, Prof. Dr. Ralf Metzler, Prof. Dr. A. Pikovsky, Prof. Dr. S. Reich, Prof. Dr. M. Rosenblum, Prof. Dr. G. Rüdiger, Prof. Dr. T. Scheffer, Prof. Dr. F. Scherbaum, Prof. Dr. J. Selbig, Prof. Dr. F. Spahn

Seminar

Speaker: Andrey Shilnikov, Mathematics and Statistics, Neuroscience, Georgia State University, USA

Title: Symbolic tools for homoclinic chaos * Oberseminar Nichtlineare Dynamik

Time: Mon, Aug 3, 2015, 2:30pm

Place: bldg 28, room 2.100

Abstract:
Over recent years, a great deal of analytical studies and modeling simulations have been brought together to identify the key signatures that allow dynamically similar nonlinear systems from diverse origins to be united into a single class. Among these key structures are bifurcations of homoclinic and heteroclinic connections of saddle equilibria. Unlike local bifurcations, global bifurcations being the organizing centers of complex behaviors in dynamical systems of any origin are still poorly understood. Such homoclinic structures are the primary cause for high sensitivity and instability of deterministic chaos in such systems. Development of effective, intelligent and yet simple algorithmic tools is an imperative task for studies of dynamics and evolution in generic nonlinear systems. Knowledge of the theory of dynamical systems and bifurcations permits us to formulate the principal and universal ideas underlying such computational tools.

Our approaches for studying these complex dynamics capitalize on а key property of most systems with deterministic chaos - recurrent, unpredictable switching between several metastable centers separated by saddle thresholds. The core of the approach is reduction of the time evolution of a characteristic observable in a system to its symbolic representation to conjugate or differentiate between similar behaviors. The pilot applications of our computational toolkit to exemplary systems have uncovered а wealth of unique and self-similar bifurcation structures, which create multi-fractal regions in the parameter space of systems with the Lorenz attractors. No other technique can reveal fine details of parametric organizations of chaos with such clarity. The toolkit will be beneficial for in-depth computational studies of any system permitting a proper phase space partition and a symbolic description. Of particular consideration are systems with the Lorenz attractor and ones with spiral chaos due to the Shilnikov saddle-focus. The proposed approach and tools will let one to detect homoclinic and heteroclinic orbits, and carry out state of the art studies of such nonlocal bifurcations in parameterized systems from diverse applications.

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Past NLD Seminars (1994-2007) & (2008 ...)

Students' seminar: Theoretical Physics, PIK, Modeling & TSA Berlin-Potsdam-Colloquia: PhysGesellschaft Berlin, TU Berlin, Pro Physik, AIP, AEI, MPI-KGF, GFZ, HMI, PIK, AWI, Max Planck Institute for the History of Science, Mathematik, DPG Disputationen, & Vorschau UP

Udo Schwarz, Zentrum für Dynamik komplexer Systeme,
Universität Potsdam, Campus Golm Karl-Liebknecht-Str. 24, 14476 Potsdam, building 28, room 2.107
Phone: (+49-331) 977-1658, Fax : (+49-331) 977-1045

Email: Udo.Schwarz AT uni-potsdam.de

DFG SFB 1294

DFG Sonderforschungsbereich 1294 Data assimilation

DFG SPP 1488

DFG Schwerpunktprogramm 1488 Planetmag


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