A nonlinear, inverted pendulum that is forced and dampled (the "Euler strut") is modeled numerically using maple. A period-doubling route to chaotic behavior is demonstrated using time series graphs, phase space plots, Poincare maps and power spectra--all obtained from Maple code. Finally, an animation of the Euler strut is demonstrated that illustrates how the system proceeds from regular motion to chaotic motion as the forcing amplitude is changed.

The ordinary predator-prey poblem can be solved using the Volterra-Lotka differential equations. The solution produces closed orbits in the phase diagram. When the number of species is greater than two, the problem becomes more interesting. Using the Volterra-Lotka equations for three species, it is possible for one of the populations to become extinct. I examined the case of one predator and two prey. By adjusting the coefficients in the Volterra-Lotka equations, I was able to produce closed orbits and spirals to extinction in the phase diagram. Based on the examples run on Maple I conclude with a conjecture on when closed orbits are obtained and when one of the prey populations becomes extinct.