Refine
Year of publication
Language
- English (293)
Is part of the Bibliography
- yes (293) (remove)
Keywords
- anomalous diffusion (51)
- diffusion (42)
- stochastic processes (12)
- living cells (9)
- ageing (6)
- first passage time (6)
- fractional Brownian motion (6)
- geometric Brownian motion (6)
- nonergodicity (6)
- Brownian motion (5)
Institute
Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades.