9: Bifurcation of Equilibria II
- Page ID
- 24192
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- 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.