28 May 2004 Analysis of biological chaotic rhythmes
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Abstract
In the paper, some chaotic one-dimensional maps modeling biological and physiological rythmes (neuron activity or heart beats) are suggested. These maps are constructed as transformations that are topologically conjugated to piecewise linear ergodic and mixing endomorphism having the uniform invariant distributions and exact trajectory characteristics (as functions of initial conditions and number of iterations). New conjugated maps are defined on infinite intervals. They have invariant distributions in the form of various types of exponential law (standard distribution and its generalizations). It is shown that dynamics of chaotic generator depend on the choice of the basic endomorphism. Hence, there are the countable set of generators of chaotic rythmes that have the same invariant distribution and conjugation function, but obtain various rates of convergence to the invariant distribution and various autocorrelation functions. Expressions for named characteristics of the chaotic generators are derived.
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Valery M. Anikin, Valery M. Anikin, Alexander F. Goloubentsev, Alexander F. Goloubentsev, } "Analysis of biological chaotic rhythmes", Proc. SPIE 5330, Complex Dynamics, Fluctuations, Chaos, and Fractals in Biomedical Photonics, (28 May 2004); doi: 10.1117/12.528923; https://doi.org/10.1117/12.528923
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