The role of phase shifts of sensory inputs in walking revealed by means of phase reduction

The role of phase shifts of sensory inputs in walking revealed by means of phase reduction 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Computational Neuroscience Springer Journals

The role of phase shifts of sensory inputs in walking revealed by means of phase reduction

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Biomedicine; Neurosciences; Neurology; Human Genetics; Theory of Computation
ISSN
0929-5313
eISSN
1573-6873
D.O.I.
10.1007/s10827-018-0681-0
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Computational NeuroscienceSpringer Journals

Published: Mar 27, 2018

References

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