Applications of temporal chaos:: sensitive dependence on initial conditions and k2-entropy on erythrocytes viscoelastic properties

The photometric readings are obtained by ektacytometry over several millions of shear elongated cells, using a home-made device called Erythrodeformeter. This time series is used to study the fractal behaviour of erythrocyte viscoelastic properties. We have only a scalar signal and no governing equations. Therefore the complete behaviour has to be reconstructed in an artificial phase space. We used the technique of time delay coordinates suggested by Takens. A numerical method based on self-affine Brownian motion is proposed to analyse sensitive dependence on initial conditions. We hypothesize that this photometric temporal series, could be modeled as a system of bounded correlated random walk. Hence, two phase spaces n-dimensional (n = 2 to 8) are generated, and used to distinguish chaotic from white noise behaviour. We have applied modified methods of Grassberger & Procaccia not only on our photometric readings but also on a pseudoaleatory series in order to check their results. It was found that while the pseudo-aleatory series is high-dimensional, our series are low-dimensional. The role of random noise and the number of data points are discussed. Finally, our results, allow us to conclude that these methods could be used to evaluate the predictability and clinical aspects of erythrocyte rheological properties.