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Hopf bifurcation
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Hopf bifurcation
In the
mathematical theory of bifurcations
, a
Hopf
or
Poincaré–Andronov–Hopf bifurcation
, named after
Henri Poincaré
,
Eberhard Hopf
, and
Aleksandr Andronov
, is a local bifurcation in which a
fixed point
of a
dynamical system
loses stability as a pair of
complex conjugate
eigenvalues
of the
linearization
around the fixed point cross the imaginary axis of the
complex plane
. Under reasonably generic assumptions about the dynamical system, we can expect to see a small-amplitude
limit cycle
branching from the fixed point.
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