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Branch Inclusion in Generic Hopf Bifurcation: General Approach
Author(s) -
Schneider K. R.,
Heinz G.
Publication year - 1991
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19910710716
Subject(s) - hopf bifurcation , mathematics , bifurcation , transcritical bifurcation , order (exchange) , saddle node bifurcation , approximations of π , bifurcation diagram , pitchfork bifurcation , amplitude , period doubling bifurcation , mathematical analysis , nonlinear system , physics , economics , finance , quantum mechanics
By using averaging transformations we determine approximations of higher order for the family of bifurcating periodic solutions in the generic case of Hopf bifurcation. These approximations permit the application of the Newton‐Kantorovič Theorem to derive inclusions of the amplitude and period.