Logistic map for the parameter range A [2.8; 4.0]. The Liapunov exponent of the logistic map is included in the bifurcation diagram allowing to associate the exponent with the bifurcation point.
| Lomas Alpha of a logistic map simulator |
Lomas is a simple simulation tool to demonstrate and study properties and statistical features of the dynamical system desribed by the Logistic Map.
It reads as follows
XT+1 = f(XT; A)
where the functional relation between future and past states is given by
f(X; A) = A X (1-X)
The parameter A ranges from 0 to 4; in the latter case this is referred to as the Ulam map.
Lomas includes the following sections:
# Time Series
# Histogram
# Bifurcation
# Liapunov Diagram, and
# Renyi Entropy of order q
For time series analysis, histogram, and Renyi entropy analysis, the external parameter A of the logistic map and/or the order q of the Renyi entropy are asked to be entered interactively. Furthermore, one may choose between a single or multiple sections.
lomas v1.01 (Alpha)
© 1998 D. Holste (Xmgr piped by D. Beule).
Downloads
Get the GZipped C source code (370 Kb),
or Mail the author
Example outputs
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Noise-free bifurcation diagram
Logistic map for the parameter range A [2.8; 4.0]. The Liapunov exponent of the logistic map is included in the bifurcation diagram allowing to associate the exponent with the bifurcation point. |
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Noise-perturbed bifurcation diagram
Logistic map for the parameter range A [2.8; 4.0]. Bifurcation diagram of the logistic map perturbed by Gaussian white noise and the corresponding Liapunov exponent. Though the bifurcation structure is smeared out, the bifurcation points remain as in the noise-free case. |
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As the island of our knowledge grows,
so does the shore of our ignorance. -John Wheeler
