Analysis of Global Dynamics from Experimental Data: Case Studies

Thursday, February 13, 2014 - 10:15am - 11:05am
Keller 3-180
Hiroshi Kokubu (Kyoto University)
I show some attempts in my research group for understanding global phase space structures of dynamics from experimental data. I will discuss the following problems as case studies.
One problem is to understand the basin of attraction of the human bipedal locomotion, where we study simple mathematical models of passive bipedal locomotion and locomotion driven by a phase oscillator, and show that there are several common features of the basin of attraction in both models. The analysis is done by numerical time series data from the models, and we explain the common features by using the hyperbolicity of the saddle equilibrium corresponding to the upright standing.
Another problem is to study transition of winter weather patterns from observed meteorological data. Here we are interested in the trend of weather pattern change. We use the idea of Morse decomposition obtained from time series analysis for observed data, as well as for numerical simulation data of General Circulation Model. The results seem to agree with common knowledge among meteorologists, and we discuss the possibility and limitation of the method.
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