as well as a graph of the slope function, f(P) = r P (1 - P/K). Click on the left-hand figure to generate solutions of the logistic equation for various starting populations P(0). [Note: The vertical coordinate of the point at which you click is considered to be P(0). The horizontal (time) coordinate is ignored.]
An equilibrium solution P = c is called stable if any solution P(t) that starts near P = c stays near it. The equilibrium P = c is called asymptotically stable if any solution P(t) that starts near P = c actually converges to it -- that is,
If an equilibrium is not stable, it is called unstable. This means there is at least one solution that starts near the equilibrium and runs away from it.