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Periodically Perturbed Bifurcation. II. Hopf Bifurcation
Author(s) -
Rosenblat S.,
Cohen Donals S.
Publication year - 1981
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1981642143
Subject(s) - quasiperiodic function , bifurcation , pitchfork bifurcation , mathematics , saddle node bifurcation , bogdanov–takens bifurcation , hopf bifurcation , transcritical bifurcation , resonance (particle physics) , mathematical analysis , perturbation (astronomy) , biological applications of bifurcation theory , bifurcation diagram , bifurcation theory , physics , nonlinear system , quantum mechanics , particle physics
We consider the effect of a periodic perturbation on the bifurcation behavior of a system of differential equations. It is shown that periodic solutions are, in general, modified into quasiperiodic solutions. Different phenomena are encountered in resonance and near‐resonance conditions, leading in some cases to separation of solution branches and in other cases to new solution branches.