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Average phase difference theory and 1:1 phase entrainment in interlimb coordination.

D Sternad1, M T Turvey, R C Schmidt

  • 1Center for the Ecological Study of Perception and Action, University of Connecticut, Storrs 06268.

Biological Cybernetics
|January 1, 1992
PubMed
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This study on coupled biological oscillators found that phase difference depends multiplicatively on frequency difference and coupling strength. These findings hold true for both in-phase and anti-phase coordination patterns.

Area of Science:

  • Dynamical systems
  • Biological physics
  • Neuroscience

Background:

  • Coupled biological oscillators are common in nature.
  • Average phase difference theory models mode locking phenomena.
  • The Rand et al. (1988) model, d phi/dt = delta omega - K sin phi, is a key theoretical framework.

Purpose of the Study:

  • To empirically evaluate phase-locking predictions from average phase difference theory.
  • To investigate the influence of frequency difference (delta omega) and coupling strength (K) on phase difference (phi).

Main Methods:

  • Three experiments used an interlimb coordination paradigm with hand-held pendulums.
  • Frequency difference (delta omega) was manipulated via pendulum length.
  • Coupled frequency (omega c) was varied using a metronome and scaled to the eigenfrequency (omega v).

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Main Results:

  • Phase difference (phi) showed a multiplicative relationship with delta omega and K.
  • When delta omega was zero, phi was consistently 0 or pi, irrespective of K.
  • When K was large, phi approximated 0 or pi, regardless of delta omega.
  • These results were consistent for both in-phase and anti-phase coordination.

Conclusions:

  • Experimental results support the predictions of average phase difference theory.
  • The ratio omega c/omega v is a more relevant frequency measure than omega c alone.
  • The multiplicative interaction between delta omega and K is crucial for understanding phase-locking dynamics.