sample questions for final posted

[bbolker]

see the web page, practice section. Version with solutions to follow.

[bbolker]

solutions posted.

[lonsdaa]

Hi Dr. Bolker,

Could you explain how to identify the directions of the flow field arrows on the phase plane in question 4? I know in one of the examples that we did in class we just inputed test values into the equations, but since parameter values aren't given here I'm not sure how to determine whether a side of a particular nullcline corresponds to the region where the derivative is negative, or where it is positive.

Thanks,

Andrew

(Also, are your Tuesday office hours on tomorrow or are those over since the semester is done?)

[bbolker]

I will hold office hours at 9:30 tomorrow.

The solid lines are the V-nullclines (the easiest way to tell is to note that V=0 is one of the solutions, and dV/dt =0 if V=0). dV/dt is a decreasing function of P (see the second term of the dV/dt equation), hence dV/dt<0 above the quadratic curve and dV/dt>0 below it; this will correspond to left-pointing flows (decreasing V) above the quadratic curve and right-pointing flows below it.

The dashed lines are the P-nullclines (again, note that dP/dt=0 if P=0). dP/dt is an increasing function of V, hence dP/dt>0 to the right of the vertical dashed line (upward-pointing flows) and dP/dt<0 to the left of the vertical dashed line (downward-pointing flows.

[bbolker]

PS office hours will be in HH 314, not LSB 336.

[lonsdaa]

Great, thank you!