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Periodically Perturbed Bifurcation—1. Simple Bifurcation
Author(s) -
Rosenblat S.,
Cohen Donald S.
Publication year - 1980
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/sapm19806311
Subject(s) - bifurcation , mathematics , saddle node bifurcation , bifurcation theory , bifurcation diagram , mathematical analysis , transcritical bifurcation , biological applications of bifurcation theory , infinite period bifurcation , perturbation (astronomy) , period doubling bifurcation , homoclinic bifurcation , bogdanov–takens bifurcation , pitchfork bifurcation , nonlinear system , physics , quantum mechanics
We consider the effect of a periodic perturbation on the bifurcation behavior of a system of differential equations. It is shown that constant solutions are modified into periodic solutions, and that the perturbations leads to the separation of solution branches. Under certain conditions the system may have no solution in the neighborhood of the bifurcation point.