Generating surrogates from recurrences

• Published in: Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 366; no. 1865; pp. 545 - 557
• Main Authors: Thiel, M, Romano, M.C, Kurths, J, Rolfs, M, Kliegl, R
• Format: Journal Article
• Language: English
• Published: London The Royal Society 28-02-2008
• Subjects: Algorithms; Biophysical Phenomena; Biophysics; Dynamical systems; Eye movements; Eye Movements - physiology; Eyes; Humans; Hypothesis Test; Matrices; Models, Biological; Models, Statistical; Null hypothesis; Oscillators; Phase Synchronization; Recurrence Plots; Significance level; Surrogacy; Surrogate Data; Time series; Trajectories; Vision Disparity - physiology
• ISSN: 1364-503X; 1471-2962
• DOI: 10.1098/rsta.2007.2109

In this paper, we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be only one centre in the brain that produces the fixational movements in both eyes or a close link between the two centres.