Transcription of Hopf bifurcation - UCL
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Hopf bifurcation - UCL
hopf bifurcationHopf bifurcation for flowsThe term hopf bifurcation (also sometimes called Poincar e-Andronov- hopf bifurcation ) refers to thelocal birth or death of a periodic solution (self-excited oscillation) from an equilibrium as a parametercrosses a critical value. It is the simplest bifurcation not just involving equilibria and therefore belongsto what is sometimes calleddynamic(as opposed tostatic) bifurcation theory. In a differential equationa hopf bifurcation typically occurs when a complex conjugate pair of eigenvalues of the linearised flowat a fixed point becomes purely imaginary. This implies that a hopf bifurcation can only occur insystems of dimension two or a periodic solution should be generated in this event is intuitively clear from Fig.
Hopf bifurcation Hopf bifurcation for flows The term Hopf bifurcation (also sometimes called Poincar´e-Andronov-Hopf bifurcation) refers to the
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