Spruce budworm steady states
This web page shows the intersections of the per capita growth rate G(x)=r(1-x/Q) and the per capita predation rate P(x)=x/(1+x^2) for the spruce budworm model dx/dt=x(G(x)-P(x)), by Ludwig, Jones and Holling (1978). I suggest that you first fix r=0.55 and use the slider to vary Q, and then investigate the effect of varying r.