Editing Logistic map (section)

==== When r < 0 ====

Since the logistic map has been often studied as an ecological model, the case where the parameter r is negative has rarely been discussed.<!--[ 58 ]--> As a decreases from 0, when −1 < r < 0, the map asymptotically approaches a stable fixed point of xf = 0, but when a exceeds −1, it bifurcates into two periodic points, and as in the case of positive values, it passes through a period doubling bifurcation and reaches chaos.<!--[ 58 ]--> Finally, when a falls below −2, the map diverges to plus infinity.<!--[ 58 ]-->

{{Image frame|width=620|content=[[File:Bifurcation diagram logistic map (-2 to 4).png|class=skin-invert-image|620px]]
|caption=Orbit diagram for parameter r from −2 to 4. The orbit diverges when the parameter a goes beyond this range, both on the negative and positive sides.|align=center}}