In the paper, the analytical method of constructing special generating functions for eigenfunctions and eigenvalues of the Perron-Frobenius operator corresponding to piece-wise symmetric one-dimensional chaotic maps is justified. Some properties of eigenfunctions are illustrated. An extension of the results for maps related with piece-wise ones by invertible nonlinear transformations is showed. The results for chaotic one-dimensional maps modeling biological and physiological rythmes (neuron activity or heart beats) and having invariant distributions in the form of various types of exponential law (standard distribution and its generalizations) are presented.

Date Published: 29 March 2005
PDF: 7 pages
Proc. SPIE 5696, Complex Dynamics and Fluctuations in Biomedical Photonics II, (29 March 2005); doi: 10.1117/12.589565

Published in SPIE Proceedings Vol. 5696:
Complex Dynamics and Fluctuations in Biomedical Photonics II
Valery V. Tuchin, Editor(s)