Study of a degenerate Bogdanov-Takens bifurcation in a family of mechanical oscillators
The authors study nonlinear second-order ordinary differential equations as models of generalized oscillators, and detect periodic behaviour by analysing the bifurcations in these oscillators. The most degenerate equilibria are considered, and a useful information is given about nontrivial oscillatory behaviours and their transitions. In particular, it is shown that a family of mechanical oscillators exhibits a codimension-3 degeneracy associated with a double-zero eigenvalue. The authors claim that their results point out some mistakes in previous papers.
nonlinear second-order ordinary differential equations
scientific article; zbMATH DE number 1445938