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On the transition from supercritical to subcritical Hopf bifurcations
Author(s) -
Chow Shui.Ne E.,
White Robert G.,
Hadeler K. P.
Publication year - 1982
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.1670040111
Subject(s) - mathematics , hopf bifurcation , bifurcation diagram , mathematical analysis , differential equation , nonlinear system , boundary value problem , supercritical fluid , bifurcation , diagram , pitchfork bifurcation , partial differential equation , thermodynamics , physics , statistics , quantum mechanics
By using the method of averaging, we give a complete Hopf bifurcation diagram when the differential equation has more than one parameter. The method is applied to a system of parabolic equations with nonlinear coupling on the boundary. This set of equations is a mathematical model which describes the normalized concentrations of substances in a solution produced by two enzymes.