Bifurcation Diagram of Logistic Map

Logistic map is a discrete time map written as

x_n+1=ax_n(1-x_n).

In spite of the simplicity of this equation, logistic map shows very complex behavior. So many studies have done.
The above figure is the bifurcation diagram which appears when parameter a is varied.

You can expand the above bifurcation diagram with the "Bifurcation diagram of the logistic map" simulator.

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Introduction to Chaos and Nonlinear Dynamics