Zahra Aminzare

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  Gait transitions in a phase oscillator model of an insect central pattern generator
  Zahra Aminzare, Phil Holmes

  Fast running insects employ a tripod gait with three legs in swing and three in stance, while slower walkers use a tetrapod gait with two legs in swing and four in stance. Fruit flies exhibit a tetrapod to tripod transition at intermediate speeds. We study the effect of stepping frequency on such gait transitions in a bursting neuron model where each cell represents a hemi-segmental thoracic circuit of the central pattern generator. Under phase reduction, the 24 ODE bursting neuron model becomes 6 coupled phase oscillators, each corresponding to a network driving one leg. Assuming that left and right legs maintain constant phase relations, we further reduce to a system describing ipsilateral phase differences defined on a torus. We show that bifurcations occur from multiple stable tetrapod gaits to a unique stable tripod gait as speed increases, and illustrate our results using data fitted to freely walking fruit flies.