Slow Passage through a Saddle-Center Bifurcation

@article{Diminnie2000SlowPT,
  title={Slow Passage through a Saddle-Center Bifurcation},
  author={David C. Diminnie and Richard Haberman},
  journal={J. Nonlinear Science},
  year={2000},
  volume={10},
  pages={197-221}
}
Slowly varying conservative one-degree of freedom Hamiltonian systems are analyzed in the case of a saddle-center bifurcation. Away from unperturbed homoclinic orbits, strongly nonlinear oscillations are obtained using the method of averaging. A long sequence of nearly homoclinic orbits is matched to the strongly nonlinear oscillations before and after the slow passage. Usually solutions pass through the separatrix associated with the double homoclinic orbit before the saddle-center bifurcation… CONTINUE READING
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