Bifurcation diagram
In mathematics, particularly in dynamical systems, a bifurcation diagram shows the possible long-term values a variable of a system can obtain in function of a parameter of the system.
An example is the bifurcation diagram of the logistic map. In this case, the parameter r is shown on the x-axis of the plot and the y-axis shows the possible long-term population values of the logistic function.
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Bifurcation diagram of a logistic map
The bifurcation diagram nicely shows the forking of the possible periods of stable orbits from 1 to 2 to 4 to 8 etc. The ratio of the lengths of successive intervals between values of r for which bifurcation occurs converges to the Feigenbaum constant. An interesting feature of this diagram is that as the periods go to infinity, r remains finite. When r is greater than (approximately) 3.57, the orbits become chaotic. Hence this bifurcation diagram demonstrates a nice example of the importance of chaos theory in even very simple non-linear systems.