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Half‐stable solution branches for ordinary bifurcation problems
Author(s) -
Beyn W.J.,
Kirchgassner K.
Publication year - 1983
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670050102
Subject(s) - mathematics , bifurcation , infinity , stability (learning theory) , order (exchange) , mathematical analysis , nonlinear system , bifurcation diagram , saddle node bifurcation , bifurcation theory , physics , finance , quantum mechanics , machine learning , computer science , economics
It is shown that second order bifurcation problems with a positive, autonomous nonlinearity have a smooth branch of positive solutions which tends to infinity. Moreover, this branch satisfies a stability rule saying that the solutions are stable if the branch turns to the right and unstable if it turns to the left.