Lyapunov Inverse Iteration for Identifying Hopf Bifurcations in Models of Incompressible Flow

@article{Elman2012LyapunovII,
  title={Lyapunov Inverse Iteration for Identifying Hopf Bifurcations in Models of Incompressible Flow},
  author={Howard C. Elman and Karl Meerbergen and Alastair Spence and Minghao Wu},
  journal={SIAM J. Scientific Computing},
  year={2012},
  volume={34}
}
The identification of instability in large-scale dynamical systems caused by Hopf bifurcation is difficult because of the problem of identifying the rightmost pair of complex eigenvalues of large sparse generalized eigenvalue problems. A new method developed in [Meerbergen and Spence, SIAM J. Matrix Anal. Appl., 31 (2010), pp. 19821999] avoids this computation, instead performing an inverse iteration for a certain set of real eigenvalues and that requires the solution of a large-scale Lyapunov… CONTINUE READING

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