The VRP-2 dynamics, with the parameter alpha value approaching the value equal to the value of the dimensionless ﬁne-structure constant, features maximum variety with regard to the number of bifurcations with the minimum degree of chaosticity.
This files contains an articles describing the Verhulst-Ricker-Planck dynamic and its relation to the fine structure constant.
The MathCAD's text program for the bifurcation diagram "four rats" (D.B.Volov, Russia, Samara).
Source code in MATLAB to reproduce the bifurcation diagram "four rats" (A.P.Trounev, Toronto, Canada)
The bifurcation diagram "four rats" one-dimensional dynamic.
Code for the Wolfram Mathematica 8 & result (A.P.Trounev, Toronto, Canada):