The Library
Symmetry-breaking in a rate model for a biped locomotion central pattern generator
Tools
Tools
Tools
Stewart, Ian (2014) Symmetry-breaking in a rate model for a biped locomotion central pattern generator. Symmetry, Volume 6 (Number 1). pp. 23-66. doi:10.3390/sym6010023 ISSN 2073-8994.
|
PDF
WRAP_symmetry-06-00023.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution. Download (4Mb) | Preview |
Official URL: http://dx.doi.org/10.3390/sym6010023
Abstract
The timing patterns of animal gaits are produced by a network of spinal neurons called a Central Pattern Generator (CPG). Pinto and Golubitsky studied a four-node CPG for biped dynamics in which each leg is associated with one flexor node and one extensor node, with Ζ2 x Ζ2 symmetry. They used symmetric bifurcation theory to predict the existence of four primary gaits and seven secondary gaits. We use methods from symmetric bifurcation theory to investigate local bifurcation, both steady-state and Hopf, for their network architecture in a rate model. Rate models incorporate parameters corresponding to the strengths of connections in the CPG: positive for excitatory connections and negative for inhibitory ones. The three-dimensional space of connection strengths is partitioned into regions that correspond to the first local bifurcation from a fully symmetric equilibrium. The partition is polyhedral, and its symmetry group is that of a tetrahedron. It comprises two concentric tetrahedra, subdivided by various symmetry planes. The tetrahedral symmetry arises from the structure of the eigenvalues of the connection matrix, which is involved in, but not equal to, the Jacobian of the rate model at bifurcation points. Some of the results apply to rate equations on more general networks.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Gait in animals, Bifurcation theory | ||||||||
| Journal or Publication Title: | Symmetry | ||||||||
| Publisher: | M D P I AG | ||||||||
| ISSN: | 2073-8994 | ||||||||
| Official Date: | 3 January 2014 | ||||||||
| Dates: |
|
||||||||
| Volume: | Volume 6 | ||||||||
| Number: | Number 1 | ||||||||
| Page Range: | pp. 23-66 | ||||||||
| DOI: | 10.3390/sym6010023 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 28 July 2016 | ||||||||
| Date of first compliant Open Access: | 28 July 2016 |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
