Complex gait disturbances represent one of the prominent manifestations of various neurophysiological conditions, including widespread neurodegenerative disorders such as Alzheimer's and Parkinson's diseases. Therefore, instrumental measurement techniques and automatic computerized analysis appears essential for the differential diagnostics, as well as for the assessment of treatment effectiveness from experimental animal models to clinical settings. Here we present a marker-free instrumental approach to the analysis of gait disturbances in animal models. Our approach is based on the analysis of video recordings obtained with a camera placed underneath an open field arena with transparent floor using the DeeperCut algorithm capable of online tracking of individual animal body parts, such as the snout, the paws and the tail. The extracted trajectories of animal body parts are next analyzed using an original computerized methodology that relies upon a generalized scalable model based on fractional Brownian motion with parameters identified by detrended partial cross-correlation analysis. We have shown that in a mouse model representative movement patterns are characterized by two asymptotic regimes characterized by integrated 1/f noise at small scales and nearly random displacements at large scales separated by a single crossover. More detailed analysis of gait disturbances revealed that the detrended cross-correlations between the movements of the snout, paws and tail relative to the animal body midpoint exhibit statistically significant discrepancies in the Alzheimer's disease mouse model compared to the control group at scales around the location of the crossover. We expect that the proposed approach, due to its universality, robustness and clear physical interpretation, is a promising direction for the design of applied analysis tools for the diagnostics of various gait disturbances and behavioral aspects in animal models. We further believe that the suggested mathematical models could be relevant as a complementary tool in clinical diagnostics of various neurophysiological conditions associated with movement disorders.