The purpose of this study is to evaluate human speech rate variability and to analyze the dynamics of spontaneous speech signals of two groups, Alzheimer's and healthy subjects, to obtain a detailed understanding of their speech pattern differences so that Alzheimer's disease can be diagnosed automatically and readily. In the approach proposed in this study, the dynamics of the speech signals are analyzed by examining the mean square error (MSE) surface and contour plots quantification of these groups. In general, the results show that the speech signals transit from a high dimensional chaotic state in control subjects to a low dimensional chaotic motion in Alzheimer's patients. This can be due to the decreased interaction of variables in psychological state. Moreover, it can be partially attributed to the fact that in AD the brain begins to shrink, with the number of brain nerve fibers gradually reducing.