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Hopf bifurcations of ODE systems along the singular direction in the parameter plane
This paper considers Hopf bifurcation of ordinary
differential systems along the singular direction in the
parameter plane. Hopf Bifurcation of the same system along non-singular directions
have been studied recently in [9]. As an application of our main results,
we also obtain results of existence and non-existence for a type of degenerate Hopf
bifurcation (i.e., the type without transversality) for one parameter ODE systems.