Consider a system:
$dx/dt = x(1-x)-\frac{kxy}{kx+1}$
$dy/dt = ry(1-\frac{y}{x})$
For values of r as 0.15, 0.11, and 0.05, which of the corresponding phase portraits displays limit cycle behavior? Is the cycle an attractor or a repeller?
I found the three portraits as:
r = 0.15
r = 0.11
r = 0.05
But I don't know how to tell which one exhibits "limit cycle behavior." Can anyone explain what this means and how I can know, by looking at each phase portrait, which is the correct answer (and whether it's a repeller or attractor)?