Phase Dynamics on the Modified Oscillators in Bipedal Locomotion

  • Wulin Weng
  • Shin-Ichiro Ei
  • Kunishige Ohgane
Part of the Mathematics for Industry book series (MFI, volume 4)


Based on neurophysiological evidence, studies modeling human locomotion system have shown that a bipedal walking is generated by mutual entrainments between the oscillatory activities of a central pattern generator (CPG) and a Body. The walking model could well reproduce human walking. However, it has been also shown that time delay in the sensorimotor loop destabilizes mutual entrainments, which leads a failure to walk. Recently, theoretical studies have discovered a phenomenon in which a CPG can induce the phase of its oscillatory activity to shift forward according to time delay. This self-organized phenomenon overcoming time delay is called “flexible-phase locking”. Then, theoretical studies have hypothesized that one of the essential mechanisms to yield of flexible-phase locking is a stable limit cycle of CPG activity. This study demonstrates the hypothesis in walking models through computer simulation by replacing the CPG model with the one having different oscillation properties.


CPG Body Time delay Limit cycle Flexible-phase locking 


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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Graduate School of MathematicsKyushu UniversityFukuokaJapan
  2. 2.Institute of Mathematics for IndustryKyushu UniversityFukuokaJapan
  3. 3.Graduate School of Human SciencesKinjo Gakuin UniversityMoriyama-ku, AichiJapan

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