A route to limit cycles via unfolding the pitchfork with feedback

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

4 Scopus citations


Motivated by the problem of developing a system that can switch between low-level control vector fields, we study the feedback interconnection of a decision mechanism based on the pitchfork bifurcation with a plant whose dynamics are given by the linear combination of two control vector fields; the state of the pitchfork system then determines the linear combination coefficients for the plant. We show how the plant state can be fed back to the pitchfork by using the Lyapunov functions of the control vector fields as an unfolding parameter in the pitchfork, and derive conditions under which the closed-loop system exhibits a Hopf bifurcation leading to stable limit cycles.

Original languageEnglish (US)
Title of host publication2019 American Control Conference, ACC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781538679265
StatePublished - Jul 2019
Event2019 American Control Conference, ACC 2019 - Philadelphia, United States
Duration: Jul 10 2019Jul 12 2019

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2019 American Control Conference, ACC 2019
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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