# Coupled nonlinear oscillators and the symmetries of animal gaits

@article{Collins1993CoupledNO, title={Coupled nonlinear oscillators and the symmetries of animal gaits}, author={James J. Collins and I. N. Stewart}, journal={Journal of Nonlinear Science}, year={1993}, volume={3}, pages={349-392} }

SummaryAnimal locomotion typically employs several distinct periodic patterns of leg movements, known as gaits. It has long been observed that most gaits possess a degree of symmetry. Our aim is to draw attention to some remarkable parallels between the generalities of coupled nonlinear oscillators and the observed symmetries of gaits, and to describe how this observation might impose constraints on the general structure of the neural circuits, i.e. central pattern generators, that control…

## 481 Citations

### Spontaneous Symmetry-Breaking in a Network Model for Quadruped Locomotion

- BiologyInt. J. Bifurc. Chaos
- 2017

This work formulates a rate model and calculates how the first steady or Ho...

### Hexapodal gaits and coupled nonlinear oscillator models

- EngineeringBiological Cybernetics
- 2004

The present analysis leads to a natural classification of hexapodal gaits by symmetry and to natural sequences of gait bifurcations, which relates observed gaits to the overall organizational structure of the underlying CPG.

### Symmetry in locomotor central pattern generators and animal gaits

- BiologyNature
- 1999

It is suggested that symmetry can be used to infer a plausible class of CPG network architectures from observed patterns of animal gaits, including a distinction between primary and secondary gait, the existence of a new primary gait called ‘jump’, and the occurrence of half-integer wave numbers in myriapod gaits.

### Coupled chaotic oscillators and their relation to a central pattern generator for artificial quadrupeds

- Biology, Engineering
- 2005

This work proposes to extend the CPG symmetries of the gaits of quadrupeds and bipeds using coupled chaotic oscillators synchronized using the Pyragas method and evaluates the time series behavior when the foot is in contact with the ground: this has potential robotic applications.

### Models of central pattern generators for quadruped locomotion I. Primary gaits

- MathematicsJournal of mathematical biology
- 2001

The proposed network of symmetrically coupled cells modeling central pattern generators for quadruped locomotion is shown to be the simplest one, and a general theorem classifying spatio-temporal symmetries of periodic solutions to equivariant systems of differential equations is proved.

### Hard-wired central pattern generators for quadrupedal locomotion

- Biology, PhysicsBiological Cybernetics
- 2004

It is demonstrated that a hard-wired CPG model, made up of four coupled nonlinear oscillators, can produce multiple phase-locked oscillation patterns that correspond to three common quadrupedal gaits — the walk, trot, and bound.

### Symmetry-Breaking in a Rate Model for a Biped Locomotion Central Pattern Generator

- MathematicsSymmetry
- 2014

Methods from symmetric bifurcation theory are used to investigate local b ifurcation, both steady-state and Hopf, for their network architecture in a rate model and apply to rate equations on more general networks.

### Models of central pattern generators for quadruped locomotion. I. Primary gaits.

- MathematicsJournal of mathematical biology
- 2001

It is shown that under mild assumptions on the cells and the coupling of the network, primary gaits can be produced from Hopf bifurcation by varying only coupling strengths of the Network of symmetrically coupled cells.

### Gait Transitions in a Phase Oscillator Model of an Insect Central Pattern Generator

- BiologySIAM J. Appl. Dyn. Syst.
- 2018

Here, the effect of stepping frequency on gait transition in an ion-channel bursting neuron model in which each cell represents a hemisegmental thoracic circuit of the central pattern generator is studied.

### Phase locking in coupled oscillators as hybrid automata

- Computer Science
- 2004

This work has mapped out the synchronization behavior of CCM networks of various topologies parametrically, and developed a section-map analysis approach that exploits the polyhedral geometry of the hybrid state space.

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