I am going through Strogatz's Nonlinear Dynamics and Chaos and am stuck on one exercise from chapter 8 (exercise 8.5.3).
The first part of the problem says:
Consider the logistic equation $\dot{N} = r N (N - N/K(t))$, where the carrying capacity is positive, smooth and T-periodic in t.
a) Using a Poincaré map argument like that in the text, show that the system has at least one stable limit cycle of period T, contained in the strip $K_{min} \leq N \leq K_{max}$
My problem, I am afraid, lays in the base interpretation of the task.
I am expecting a 2D system, and instead I can only see one differential equation and one extra function ($F(t)$), for which I can't extrapolate any information about the derivative. I am baseically not able to draw the phase plane or sketch the vector field.
I am quite lost on how to start this exercise, but I would like to work on it. Does anyone have any ideas on how to interpret it?