Random walks, random sequences, and nonlinear dynamics in human optokinetic nystagmus

P. Trillenberg, C. Gross, M. Shelhamer

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Optokinetic nystagmus (OKN) is a reflexive eye movement with target-following slow phases (SP) alternating with oppositely directed fast phases (FP). We measured the following from OKN in three humans: FP beginning and ending positions, amplitudes, and intervals and SP amplitudes and velocities. We sought to predict future values of each parameter on the basis of past values, using state-space representation of the sequence (time-delay embedding) and local second-order approximation of trajectories. Predictability is an indication of determinism: this approach allows us to investigate the relative contributions of random and deterministic dynamics in OKN. FP beginning and ending positions showed good predictability, but SP velocity was less predictable. FP and SP amplitudes and FP intervals had little or no predictability. FP beginnings and endings were as predictable as randomized versions that retain linear autocorrelation; this is typical of random walks. Predictability of FP intervals did not change under random rearrangement, which is characteristic of a random process. Only linear determinism was demonstrated; nonlinear interactions may exist that would not be detected by our present approach.

Original languageEnglish (US)
Pages (from-to)1750-1759
Number of pages10
JournalJournal of applied physiology
Issue number4
StatePublished - 2001


  • Fractal scaling
  • Prediction
  • Vestibulo-ocular reflex

ASJC Scopus subject areas

  • Physiology
  • Physiology (medical)


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