Inverse iteration for purely imaginary eigenvalues with application to the detection of Hopf bifurcations in large scale problems KU Leuven
The detection of a Hopf bifurcation in a large scale dynamical system that depends on a physical parameter often consists of computing the right-most eigenvalues of a sequence of large sparse eigenvalue problems. Guckenheimer et. al. (SINUM, 34, (1997) pp. 1-21) proposed a method that computes a value of the parameter that corresponds to a Hopf point without actually computing right-most eigenvalues. This method utilises a certain sum of ...