Journal article
Gait transitions in a phase oscillator model of an insect central pattern generator
SIAM Journal on Applied Dynamical Systems, Vol.17(1), pp.626-671
2018
DOI: 10.1137/17M1125571
Abstract
Legged locomotion involves various gaits. It has been observed that fast running insects (cockroaches) employ a tripod gait with three legs lifted off the ground simultaneously in swing, while slow walking insects (stick insects) use a tetrapod gait with two legs lifted off the ground simultaneously. Fruit flies use both gaits and exhibit a transition from tetrapod to tripod at intermediate speeds. Here we study the effect of stepping frequency on gait transition in an ion-channel bursting neuron model in which each cell represents a hemi-segmental thoracic circuit of the central pattern generator. Employing phase reduction, we reduce the network of bursting neurons represented by 24 ordinary differential equations to 6 coupled nonlinear phase oscillators, each corresponding to a sub-network of neurons controlling one leg. Assuming that the left and right legs maintain constant phase differences (contralateral symmetry), we reduce from 6 equations to 3, allowing analysis of a dynamical system with 2 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. Finally, we consider gait transitions in two sets of data fitted to freely walking fruit flies.
Details
- Title: Subtitle
- Gait transitions in a phase oscillator model of an insect central pattern generator
- Creators
- Zahra AminzareVaibhav SrivastavaPhilip Holmes
- Resource Type
- Journal article
- Publication Details
- SIAM Journal on Applied Dynamical Systems, Vol.17(1), pp.626-671
- DOI
- 10.1137/17M1125571
- ISSN
- 1536-0040
- eISSN
- 1536-0040
- Grant note
- DOI: 10.13039/100000065, name: National Institute of Neurological Disorders and Stroke, award: U01-NS090514-01; DOI: 10.13039/100000001, name: National Science Foundation, award: DMS-1430077
- Language
- English
- Date published
- 2018
- Academic Unit
- Iowa Neuroscience Institute; Mathematics
- Record Identifier
- 9983985863102771
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