The human brain has been described as a complex system. Its study by means of neurophysiological signals has revealed the presence of linear and nonlinear interactions. In this context, entropy metrics have been used to uncover brain behavior in the presence and absence of neurological disturbances. Entropy mapping is of great interest for the study of progressive neurodegenerative diseases such as Alzheimer’s disease. The aim of this study was to characterize the dynamics of brain oscillations in such disease by means of entropy and amplitude of low frequency oscillations from Bold signals of the default network and the executive control network in Alzheimer’s patients and healthy individuals, using a database extracted from the Open Access Imaging Studies series. The results revealed higher discriminative power of entropy by permutations compared to low-frequency fluctuation amplitude and fractional amplitude of low-frequency fluctuations. Increased entropy by permutations was obtained in regions of the default network and the executive control network in patients. The posterior cingulate cortex and the precuneus showed differential characteristics when assessing entropy by permutations in both groups. There were no findings when correlating metrics with clinical scales. The results demonstrated that entropy by permutations allows characterizing brain function in Alzheimer’s patients, and also reveals information about nonlinear interactions complementary to the characteristics obtained by calculating the amplitude of low frequency oscillations.