Asymptotic Analysis of Subcritical Hopf-Homoclinic Bifurcation

  title={Asymptotic Analysis of Subcritical Hopf-Homoclinic Bifurcation},
  author={John Guckenheimer and Allan R. Willms}
This paper discusses the mathematical analysis of a codimension two bifurcation determined by the coincidence of a subcritical Hopf bifurcation with a homoclinic orbit of the Hopf equilibrium. Our work is motivated by our previous analysis of a Hodgkin-Huxley neuron model which possesses a subcritical Hopf bifurcation [5]. In this model, the Hopf bifurcation has the additional feature that trajectories beginning near the unstable manifold of the equilibrium point return to pass through a small… CONTINUE READING