Interactions of Andronov-Hopf and Bogdanov-Takens Bifurcations

@inproceedings{Zhan1998InteractionsOA,
  title={Interactions of Andronov-Hopf and Bogdanov-Takens Bifurcations},
  author={Kai Zhan},
  year={1998}
}
A codimension-three bifurcation, characterized by a pair of purely imaginary eigenvalues and a nonsemisimple double zero eigenvalue, arises in the study of a pair of weakly coupled nonlinear oscillators with Z2 Z2 symmetry. The methodology is based on Arnold's ideas of versal deformations of matrices for the linear analysis, and Poincar e normal forms for the nonlinear analysis of the system. Bifurcation submanifolds of codimension one and two are identi ed in the parameter space. Many di erent… CONTINUE READING
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