Institute for Computational Neuroscience

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Universal Scaling Behavior and Fractal Geometry

 In the first part of our seminar, we will investigate the period doubling transition to chaos in the 2D invertible Henon Map and the forced pendulum, and the universality of the critical scaling behavior found in the 1D Map will be examined. In the second part, we will characterize the fractal geometry of the chaotic attractor that appears in the 2D Henon Map in terms of various fractal dimensions.

1. Universality for The Period-Doubling Transition to Chaos 

   1.1 Period Doublings in the Henon Map

     1.1.1 Finding periodic orbits and their stability analysis. E.-S. Lee (Mar. 23, 2002).[ PPT ]

     1.1.2 Lyapunov exponents in the 2D Henon map. E.-S. Lee (Mar. 30,2002). [ PPT ]

     1.1.3 Confirmation of the universality of the critical scaling behaviors. E.-S. Lee (Apr. 6, 2002). [ PPT ]

   1.2 Period Doublings in the Parametrically Forced Pendulum

     1.2.1 Poincaré maps of the parametrically forced pendulum. E.-S. Lee (Apr. 27, 2002).[ PPT ]

     1.2.2 Finding periodic orbits and their stability analysis. E.-S. Lee (May. 4, 2002).[ PPT ]

     1.2.3 Confirmation of the universality of the critical scaling behaviors. E.-S. Lee (May 11, 2002).[ PPT ]

2. Characterization of the strange chaotic attractor in the 2D Henon map

2.1 Capacity dimension. E.-S. Lee(May 18, 2002).[ PPT ]

2.2 Information dimension. E.-S. Lee(May 25, 2002).

   2.3 Correlation dimension. E.-S. Lee (Jun. 1,2002).

Final Report

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