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@ARTICLE{Yeldesbay:844848,
      author       = {Yeldesbay, Azamat and Tóth, Tibor and Daun, Silvia},
      title        = {{T}he role of phase shifts of sensory inputs in walking
                      revealed by means of phase reduction -},
      journal      = {Journal of computational neuroscience},
      volume       = {44},
      number       = {3},
      issn         = {0929-5313},
      address      = {Dordrecht [u.a.]},
      publisher    = {Springer Science + Business Media B.V},
      reportid     = {FZJ-2018-02199},
      pages        = {313–339},
      year         = {2018},
      abstract     = {Detailed neural network models of animal locomotion are
                      important means to understand the underlying mechanisms that
                      control the coordinated movement of individual limbs.
                      Daun-Gruhn and Tóth, Journal of Computational Neuroscience
                      31(2), 43–60 (2011) constructed an inter-segmental network
                      model of stick insect locomotion consisting of three
                      interconnected central pattern generators (CPGs) that are
                      associated with the protraction-retraction movements of the
                      front, middle and hind leg. This model could reproduce the
                      basic locomotion coordination patterns, such as tri- and
                      tetrapod, and the transitions between them. However, the
                      analysis of such a system is a formidable task because of
                      its large number of variables and parameters. In this study,
                      we employed phase reduction and averaging theory to this
                      large network model in order to reduce it to a system of
                      coupled phase oscillators. This enabled us to analyze the
                      complex behavior of the system in a reduced parameter space.
                      In this paper, we show that the reduced model reproduces the
                      results of the original model. By analyzing the interaction
                      of just two coupled phase oscillators, we found that the
                      neighboring CPGs could operate within distinct regimes,
                      depending on the phase shift between the sensory inputs from
                      the extremities and the phases of the individual CPGs. We
                      demonstrate that this dependence is essential to produce
                      different coordination patterns and the transition between
                      them. Additionally, applying averaging theory to the system
                      of all three phase oscillators, we calculate the stable
                      fixed points - they correspond to stable tripod or tetrapod
                      coordination patterns and identify two ways of transition
                      between them.},
      cin          = {INM-3},
      ddc          = {610},
      cid          = {I:(DE-Juel1)INM-3-20090406},
      pnm          = {572 - (Dys-)function and Plasticity (POF3-572)},
      pid          = {G:(DE-HGF)POF3-572},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:29589252},
      UT           = {WOS:000433484800003},
      doi          = {10.1007/s10827-018-0681-0},
      url          = {https://juser.fz-juelich.de/record/844848},
}