A study is made of differential equations which have low-frequency periodic bifurcating solutions. It is shown that the classical Poincaré-Hopf technique for constructing periodic solutions encounters difficulties in the low-frequency limit, and that the branches are determined by nonlinear, rather than linear, balances. Two types of models are investigated: one is autonomous and the other non-autonomous, with a forcing term of small, fixed frequency. The latter model is relevant to several fluid-dynamical situations.
ASJC Scopus subject areas
- Applied Mathematics