Everything about Bifurcation Diagram totally explained
In
mathematics, particularly in
dynamical systems, a
bifurcation diagram shows the possible long-term values (equilibria/fixed points or periodic orbits) of a system as a function of a
bifurcation parameter in the system. It is usual to represent stable solutions with a solid line and unstable solutions with a dotted line.
Bifurcations in the Logistic Map
An example is the bifurcation diagram of the
logistic map:
» ,
which is
structurally stable when
, if a bifurcation diagram is plotted, treating
as the bifurcation parameter, but for different values of
, the case
is the symmetric pitchfork bifurcation. When
, we say we've a pitchfork with
broken symmetry. This is illustrated in the animation on the right.
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