Effect of a Perturbation on the Stable Points of a Dynamical System

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A bifurcation diagram illustrates how the fixed points in a first-order dynamical system evolve as a function parameter changes. Take any vertical line upwards (along the dimension) and note the fixed points at the color boundaries. From brown to purple is a stable point; from purple to brown is an unstable point. The default situation in this example shows a subcritical pitchfork bifurcation. A non-symmetrical perturbation , added with the slider control, changes the system behavior and its bifurcation diagram.

Contributed by: Andrew Read (December 2008)
After work by: Steven H. Strogatz
Open content licensed under CC BY-NC-SA


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