Criterion to identify Hopf bifurcations in maps of arbitrary dimension.

  title={Criterion to identify Hopf bifurcations in maps of arbitrary dimension.},
  author={Guilin Wen},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={72 2 Pt 2},
  • Guilin Wen
  • Published 2005 in
    Physical review. E, Statistical, nonlinear, and…
The classical Hopf bifurcation criterion is stated in terms of the properties of eigenvalues. In this paper, a criterion without using eigenvalues is proposed for maps of arbitrary dimension. The parameter mechanism of Hopf bifurcation may be explicitly formulated on the basis of the criterion. A numerical example demonstrates that the proposed criterion is preferable to the classical Hopf bifurcation criterion in theoretical analysis and practical applications. 

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