Journal of Computational Neuroscience

, Volume 7, Issue 2, pp 99–118 | Cite as

Evolution and Analysis of Model CPGs for Walking: I. Dynamical Modules

  • Hillel J. Chiel
  • Randall D. Beer
  • John C. Gallagher

Abstract

Can one develop an abstract description of the dynamics of pattern generators that provides quantitative insight into their operation? We explored this question by examining the dynamics of a model central pattern generator that was created using an evolutionary algorithm. We propose an abstract description based on the concept of a dynamical module, a set of neurons that simultaneously make their transitions from one quasistable state to another while the synaptic inputs that they receive from other neurons remain essentially constant, thus temporarily reducing the dimensionality of the circuit dynamics. Using the mathematical tools of dynamical systems theory, we describe a method for identifying dynamical modules and demonstrate that this concept can be used to quantitatively characterize constraints on neural architecture, account for phase durations, and predict the effects of parameter changes. Moreover, this abstract description reveals coordinated parameter changes that leave the overall circuit dynamics essentially unchanged. In a companion article we employ this abstract description to examine the relationship between general principles and individual variability in large populations of evolved model pattern generators.

central pattern generators dynamical modules circuit building blocks dynamical systems theory 

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Hillel J. Chiel
    • 1
  • Randall D. Beer
    • 2
  • John C. Gallagher
    • 3
  1. 1.Department of Biology and Department of NeuroscienceCase Western Reserve UniversityCleveland
  2. 2.Department of Computer Engineering and Department of Biology and ScienceCase Western Reserve UniversityCleveland
  3. 3.Department of Computer ScienceSUNY Institute of Technology of Utica/RomeUtica

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