How do I adjust model parameters to get stable oscillations with Arditi-Ginzburg equations? I am using the predator-prey equations from the Arditi-Ginzburg to model the interactions of 14 species in a video game.  The equations for two species are:
$$
dx=x(A-Bx)-Cxy/(x+y)\\
dy=-Gy+Mxy/(x+y)
$$
with careful selection of parameters A,B,C,G,M I get the expected out-of-phase oscillations between the two species, but there is a damping factor.  See the plot. 

A,B: controls the growth of the prey w/o predator

C controls how fast the predator consumes the prey

G controls how fast the predator dies w/o prey

M controls how fast the predator grows with maximum prey

How can I adjust the parameters to make the oscillations continue indefinitely?  Stable systems are very common, and damped oscillations are common.  Where are the infinite oscillations?

P.S. Most choices for parameters quickly result in a stable system.. why?

Edit: With lots of tweaking, here are repeating cycles, with growing amplitude, see plot.

Increasing parameter A from 0.21 to 0.23 and then increasing parameter C from 0.7 to 0.82 made the difference.  The slightly increasing amplitude can be adjusted by increasing Parameter G very slightly.

Now the peaks are fine, but the valleys are too low and too long.  I am using LibreOffice to synthesize and visualize this.  Can you guys recommend better open source tools for hacking functions?
UPDATE

I added one more predator to the mix.

$$
dx=x(A-Bx)-Cxy/(x+y)\\
dy=-Gy+Mxy/(x+y)-C1yz/(y+z)\\
dz=-G1y+M1yz/(y+z)
$$
dx= change in grass population 

dy= change in mice population

dz= change in fox population

Starting Parameters:

X=1000 Y=1000 Z=100
A= 0.23 B=0.00001 C=0.82 G=0.53 M=0.71 C1=0.42 G1=0.4 M1=0.71

The plot shows the basic out-of-phase relationships are starting to emerge, and the populations are headed towards a steady state.  A little more tweaking should get these three into steady oscillations, and then I will continue adding to the food chain...
UPDATE

I added one more predator to the mix.

$$
dx=x(A-Bx)-Cxy/(x+y)\\
dy=-Gy+Mxy/(x+y)-C1yz/(y+z)\\
dz=-G1y+M1yz/(y+z)
$$
dx= change in grass population 

dy= change in mice population

dz= change in fox population

Starting Parameters:

X=1000 Y=1000 Z=100
A= 0.23 B=0.00001 C=0.82 G=0.53 M=0.71 C1=0.42 G1=0.4 M1=0.71

The plot shows the basic out-of-phase relationships are starting to emerge, and the populations are headed towards a steady state.  A little more tweaking should get these three into steady oscillations, and then I will continue adding to the food chain...