Processing math: 100%
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

9: Bifurcation of Equilibria II

( \newcommand{\kernel}{\mathrm{null}\,}\)

  • 9.1: Bifurcation of Equilibria II
    The Poincaré-Andronov-Hopf bifurcation is very important in applications and is a bifurcation of a fixed point of an autonomous vector field where the fixed point is nonhyperbolic as a result of the Jacobian having a pair of purely imaginary eigenvalues, ±iw,w≠0 . Therefore this type of bifurcation requires (at least two dimensions), and it is not characterize by a change in the number of fixed points, but by the creation of time dependent periodic solutions.
  • 9.2: Problem Set


This page titled 9: Bifurcation of Equilibria II is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Stephen Wiggins via source content that was edited to the style and standards of the LibreTexts platform.

Support Center

How can we help?