Coupled nonlinear oscillators and the symmetries of animal gaits |
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Authors: | J J Collins I N Stewart |
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Institution: | (1) Oxford Orthopaedic Engineering Centre, Nuffield Orthopaedic Centre, University of Oxford, OX3 7LD Headington, Oxford, UK;(2) NeuroMuscular Research Center and Department of Biomedical Engineering, Boston University, 02215 Boston, MA, USA;(3) Nonlinear Systems Laboratory, Mathematics Institute, University of Warwick, CV4 7AL Coventry, UK |
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Abstract: | Summary Animal locomotion typically employs several distinct periodic patterns of leg movements, known as gaits. It has long been
observed that most gaits possess a degree of symmetry. Our aim is to draw attention to some remarkable parallels between the
generalities of coupled nonlinear oscillators and the observed symmetries of gaits, and to describe how this observation might
impose constraints on the general structure of the neural circuits, i.e. central pattern generators, that control locomotion.
We compare the symmetries of gaits with the symmetry-breaking oscillation patterns that should be expected in various networks
of symmetrically coupled nonlinear oscillators. We discuss the possibility that transitions between gaits may be modeled as
symmetry-breaking bifurcations of such oscillator networks. The emphasis is on general model-independent features of such
networks, rather than on specific models. Each type of network generates a characteristic set of gait symmetries, so our results
may be interpreted as an analysis of the general structure required of a central pattern generator in order to produce the
types of gait observed in the natural world. The approach leads to natural hierarchies of gaits, ordered by symmetry, and
to natural sequences of gait bifurcations. We briefly discuss how the ideas could be extended to hexapodal gaits. |
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Keywords: | central pattern generators locomotion gait transitions quadrupeds bifurcation |
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