|
| |
| M.T. Rosenstein and J.J. Collins. Visualizing the effects of filtering chaotic signalsComputers and Graphics 18(4):587-592, 1994. | |
| Abstract: It is well-known that filtered chaotic signals can exhibit increases in observed fractal dimension. However, there is still insufficient knowledge regarding the underlying causes of this phenomenon. We provide further insight into this problem through the use of computer animations and three-dimensional ray-tracings. Specifically, we show that lowpass filters can induce a nonuniform convergence to a dynamical system's mean state-space location. With chaotic attractors, this convergence distorts the attractor's normal geometrical configuration such that the observed system acquires increased dimensionality. | |
| Download: pdf (998KB), ps.gz (1387KB) | |
| See also: | |
|
Reconstruction expansion as a geometry-based framework for choosing
proper delay times | |
|
A practical method for calculating largest
Lyapunov exponents from small data sets |
|
|
updated 18-Jan-2001 mtr@cs.umass.edu |