A phase diagram of population dynamics, prepared at the request of students who needed to understand the diagrams presented in "Consequential classes of resources: Subtle global bifurcation with dramatic ecological consequences in a simple population model", John Vandermeer and Aaron King, [i]Journal of Theoretical Biology[/i] 263 (2010) 237–241. Time-derivatives are as given in Eq 5 of the article. They were integrated via a second-order Runga-Kutta technique to obtain trajectories of the C vs. R point. The blue slope field is for dC/dR (=[dC/dt)/(dR/dt)]), and the zero-growth isoclines are per Equation 6 of the article.

Move the "Initial Condition" point and vary the parameters to understand the importance of isoclines and the nature of their points of intersection.