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Hopf bifurcations of ODE systems along the singular direction in the parameter plane

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  • 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.
    Mathematics Subject Classification: Primary82D10,76X05,35B60,35B40.

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