Posted by Vlad on January 06, 2003 at 09:16:30:
In Reply to: How Can I use “Chaos Analyzer” for real problems? posted by Iren on January 04, 2003 at 14:32:13:
:A. I have a system of nonlinear differential equations with a chaotic attractor.
: How can I determine properties of this attractor with your “Chaos Analyzer”?
1. By means of Poincare section’s method reduce your dynamical system to a one-dimensional map.
2. Approximate the one-dimensional map with a piecewise-linear map.
3. Enter parameters of the map into the program and run calculations.
B. I have a data of experimental measurements x(n) n=1,N. Under assumption that the real process/phenomenon may be modeled by nonlinear dynamical system, can I use “Chaos Analyzer” to find properties of the process?
1. Reconstruct the one-dimensional map from the data (plot points a(n)=(x(n),x(,n+1) ) n=1,N on a plane and then build a piecewise-linear map fitted to this data)
2. Enter parameters of the map into the program and run calculations.