Eye movement dynamics during imposed fixations

Eye movement is one of the key biological signals through which further analysis may reveal substantial information enabling greater understanding the biology of the brain and its mechanisms. Several methods for such signal processing have been developed, however new solutions are being continuously sought. This paper presents analysis of one of the main eye movement components – fixation – by usage of nonlinear time series methods. This analysis, aimed at determining the existence of chaotic behaviour, indicated by many biological systems, was based on an experiment utilising ’jumping point’ stimulus. 29 stimuli were used – presented for 3 secs in different screen positions. 24 subjects participated in the experiment consisting of two sessions conducted with a two–month interval; thus the experimental dataset included 48 recordings. The first derivative of the horizontal positions of eye movement coordinates registered during a fixation served as the time series used for reconstruction of eye movement dynamics. The analysis was performed by means of the Largest Lyapunov Exponent. Its values were studied in various time scopes of a fixation duration. A positive averaged value of this exponent, indicating chaotic behaviour, was observed for the first 200 points in the case of all studied time series. In the remining of the analysed scopes negative average exponent values were shown, however, for a number of users the eye movement signal behaviour was changing from convergent to chaotic and conversely. Additionally, the user's eye movement dynamic was compared between sessions to check for the existence of any idiosyncratic features. The results revealed similarity existence for 30%–80% of participants depending on the analysed factor.