Two paths to finding the pitchfork bifurcation in motivation dynamics

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

We perform two different model reduction techniques on a dynamical system recently used to develop mechanisms for switching between low-level control vector fields. Both techniques result in the same reduced model which is shown to be a one-parameter unfolding of the supercritical pitchfork bifurcation. The first technique uses singular perturbation to reduce the original two-dimensional system to a one-dimensional system whose vector field is a rational polynomial. The second technique uses the Lyapunov-Schmidt reduction to find another one-dimensional system. In a singular limit analogous to that of the first technique, the Lyapunov-Schmidt reduced dynamics are identical to the rational polynomial found directly through singular perturbation. A nonlinear time scaling argument then shows that the rational polynomial is equivalent to a normal form for the unfolding of the pitchfork.

Original languageEnglish (US)
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages8030-8035
Number of pages6
ISBN (Electronic)9781728113982
DOIs
StatePublished - Dec 2019
Externally publishedYes
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: Dec 11 2019Dec 13 2019

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2019-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
Country/TerritoryFrance
CityNice
Period12/11/1912/13/19

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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