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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.
Leonard Lipkin and David Smith, "Logistic Growth Model - Equilibria," Convergence (December 2004)
Journal of Online Mathematics and its Applications