Hopf bifurcation calculations in delayed systems with translational symmetry

G. Orosz, G. Stépán

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

The Hopf bifurcation of an equilibrium in dynamical systems consisting of n equations with a single time delay and translational symmetry is investigated. The Jacobian belonging to the equilibrium of the corresponding delay-differential equations always has a zero eigenvalue due to the translational symmetry. This eigenvalue does not depend on the system parameters, while other characteristic roots may satisfy the conditions of Hopf bifurcation. An algorithm for this Hopf bifurcation calculation (including the center-manifold reduction) is presented. The closed form results are demonstrated for a simple model of cars following each other along a ring.

Original languageEnglish
Pages (from-to)505-528
Number of pages24
JournalJournal of Nonlinear Science
Volume14
Issue number6
DOIs
Publication statusPublished - Dec 2004

Fingerprint

Translational symmetry
Hopf bifurcation
Hopf Bifurcation
Center Manifold Reduction
Eigenvalue
Characteristic Roots
Delay Differential Equations
Time Delay
Time delay
Dynamical systems
Closed-form
Differential equations
Railroad cars
Dynamical system
Ring
Zero
Model

Keywords

  • carfollowing model
  • center-manifold
  • Infinite-dimensional system
  • relevant zero eigenvalue

ASJC Scopus subject areas

  • Applied Mathematics
  • Modelling and Simulation
  • Engineering(all)

Cite this

Hopf bifurcation calculations in delayed systems with translational symmetry. / Orosz, G.; Stépán, G.

In: Journal of Nonlinear Science, Vol. 14, No. 6, 12.2004, p. 505-528.

Research output: Contribution to journalArticle

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