The following results were obtained using Mathcad . You can view (and modify) the mathcad solution file if you have a the mathcad software (just be sure your mathcad preferences are set to view .mcd files with mathcad and click on lotka.mcd).

Elementary Runge-Kutta numerical integration was used to solve the coupled differential equations. The time range was taken to be 0<t<700 and this interval was divided into 2000 steps.

Oscillations of the concentrations of both intermediates, X and Y, were found to have a period of about 350 (arbitrary units). Logarithms of the concentrations were used to construct a plot of pX=-log([X]) and pY=-log([Y]) versus time:

The trajectory of these oscillations was then plotted in concentration space: