Publication 2012

Le Van Quyen M., Martinerie J., Adam C., Schuster H. & Varela F. J. (1997) Unstable periodic orbits in human epileptic acivity. Physical Review E 56: 3401–3411.
We examine in detail subdural recordings from a patient with an epileptic focal seizure, highly unusual in the ongoing nature of the discharges and in the lack of cognitive impairment. We applied a recent method for detecting unstable periodic orbits to the series of time intervals between successive spike discharges, and report that a few unstable fixed points exist within their apparent random fluctuations. The statistical significance of this underlying deterministic dynamics is assessed using surrogate data. In particular, the approaches of trajectories toward the unstable periodic patterns are observed in the sequences immediately following the perceptual tasks. This suggests that the act of perception contributes in a highly specific manner to pulling the epileptic activities towards particular unstable periodic orbits, which closely resemble the technique called chaos control for stabilization of unstable periodic orbits.
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