Bifurcation Diagram of Logistic Map

Logistic map is a discrete time map written as


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