Global stability of synchronous and out-of-phase oscillations in central pattern generators

Details Global stability of synchronous and out-of-phase oscillations in central pattern generators Global stability of synchronous and out-of-phase oscillations in central pattern generators

2010-12-08

arxiv.org/abs/1012.1788v1

Physics

Biological Physics

Scientific paper

Coupled arrays of Andronov-Hopf oscillators are investigated. These arrays can be diffusively or repulsively coupled, and can serve as central pattern generator models in animal locomotion and robotics. It is shown that repulsive coupling generates out-of-phase oscillations, while diffusive coupling generates synchronous oscillations. Specifically, symmetric solutions and their corresponding amplitudes are derived, and contraction analysis is used to prove global stability and convergence of oscillations to either symmetric out-of-phase or synchronous states, depending on the coupling constant. Next, the two mechanisms are used jointly by coupling multiple arrays. The resulting dynamics is analyzed, in a model inspired by the CPG-motorneuron network that controls the heartbeat of a medicinal leech.

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