Bifurcation Diagram for the cubic map and a realistic model for population dynamics

Computes bifurcation diagram

The programs compute the bifurcation diagram for the cubic map and a realistic population dynamics model. The value of parameter r, when the cycle of period three appears, is indicated. As expected, for higher values of r, we observe chaotic behaviour. Both models are given in the problems? section (problems 2.34 and 2.35; page 207) in Varma and Morbidelli, Mathematical Methods in Chemical Engineering, Oxford University Press, 1997. This work was inspired by the notebook of Professor Brian Higgins, U C Davis, who studied the logistic map: http://www.higgins.ucdavis.edu/chemmath.php . A similar treatment using Mathematica can be found at: http://library.wolfram.com/infocenter/MathSource/6614/ .