TY - JOUR
T1 - On Bifurcating Periodic Solutions at Low Frequency
AU - Davis, Stephen H.
AU - Rosenblat, S.
N1 - Publisher Copyright:
© 2015 Wiley Periodicals, Inc., A Wiley Company.
PY - 1977/7/1
Y1 - 1977/7/1
N2 - 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.
AB - 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.
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U2 - 10.1002/sapm197757159
DO - 10.1002/sapm197757159
M3 - Article
AN - SCOPUS:0002385009
SN - 0022-2526
VL - 57
SP - 59
EP - 76
JO - Studies in Applied Mathematics
JF - Studies in Applied Mathematics
IS - 1
ER -