The difficulties encountered in developing mathematical models for quantitatively describing the “physiological complexity” of the human body during development, including pathologies and exposure to physical factors are discussed. An original approach to the statistical analysis of physiological temporal signals—the Memory Functions Formalism—is being developed to study the processes of biological aging and the decrease in the body's resistance. This approach is used to analyze the temporal signals of the neuromuscular system of the subjects of various age groups: 20–24 years old, 64–69 years old, and 75–90 years old. The critical role of statistical memory effects and relaxation patterns in hand–eye coordination with increasing subject age is demonstrated. The results of statistical analysis of memory effects and relaxation parameters for electrocardiographic and electromyographic recordings for subjects of different age groups are given. For quantitative assessment of the influence of external factors on the human body, the analysis of bioelectrical activity of the cerebral cortex during exposure to external flickering stimuli of different color combinations is carried out. It has been demonstrated that visual stimulation leads to changes in frequency-phase synchronization between certain regions of the human cortex. The perspectives of using the obtained results for solving the problems of space medicine, in particular, for studying the impact of space on the human body and reducing the time for restoring the functional capabilities of astronauts after long space missions are discussed.