r-Parameter: a new measure of nonstationarity

It is known that the addition of impulses to a signal, say electroencephalogram (EEG), increases the nonstationarity of the latter. A quantitative index of the change in the nonstationarity may serve as a diagnostic parameter. The logistic equation of the form y(n)=y(n-1)exp{r[1-y(n-1)]} is used here and EEG is fitted with it for least mean square error with r as a parameter. Since this logistic equation starts exhibiting randomness from r=2.6924 and onwards, a measure of randomness is obtained. It is shown that both the correlation dimension (cd) of chaos modelling and r vary in a similar way within a limited range of r between 2.5 and 3.0.