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Graded Final Exam Student ELIZABETH GAGEA Total Points 98.5 / 112 pts Question 1 Sturgeon and carp model 6 / 10 pts  − 0 pts Correct description 1 Error (C' = 0.6 C (1-C/50k) ....  − 1 pt Per capita not correctly done  − 1 pt Description 3 error (C' = -0.4JC).  − 1 pt Description 7, introduction of healthy sturgeons not included/wrong location (J'= +150) Description 8 maturation rate assumption wrong (M' = 0.067J, J' = -0.067J)  − 0.5 pts 0.067J term incorrect, number/ state variables/additional term included  − 0.5 pts 0.067J term not included in both M' and J' Question 2 Coyote prey switching model 9 / 10 pts Voles eaten 1.3 * (diet fraction) * C(max point loss -1.5)  − 0.5 pts Didn't use sigmoid from previous steps in some form. (either a sigmoid present or (1-sigmoid). Coyote birth rate (0.4 * (voles eaten + rabbits eaten)) (max points lost = -1)  − 0.5 pts extra or missing state variables that are already included from previous steps. If no sigmoid terms are present in the rest of the problem, state variables multiplied aren't accepted.  didn't include the C variables from previously in 0.4 * (amount eaten) from previous steps. Question 3 Protein trajectory 6 / 6 pts  − 0 pts Correct 

Question 4 Swimming integration 13 / 14 pts 4.1 Approximate distance 8 / 8 pts  − 0 pts Correct. Left Riemann V(0)*2 + V(2)*2 = 10.5 or right Riemann V(2)*2 + V(4)*2 = 3.5 or middle Riemann V(1)*2 + V(3)*2 = 7 4.2 Graphical interpretation 3 / 4 pts  − 1 pt Vertical axis values too tall / too short  Second rectangle too tall 4.3 Improving approximation 2 / 2 pts  − 0 pts Correct: We can improve using smaller step sizes Question 5 Snowy plover equilibria 12 / 12 pts 5.1 Find equilibria 4 / 4 pts  − 0 pts Correct ( ) 5.2 Choose test points 4 / 4 pts  − 0 pts Correct based on (a) ( NO, we cannot determine the stability of any EPs . These test points don't work at all because there must be only one equilibrium point between two adjacent test points) 1. Between and There are no equilibrium point to be tested between X=5 and X=15, so we can't check the stability. 2. Between and There are two equilibrium points ( and ) between X=15 and X=25, so we can't check the stability. 5.3 Find stability 4 / 4 pts  − 0 pts Correct based on (a) ( : Stable, : Unstable, : Stable, : Unstable) X = 0, X = 0.02, X = 20.5, X = 21 X = 5 X = 15 → X = 15 X = 25 → X = ∗ 20.5 X = ∗ 21 X = 0 X = 0.02 X = 20.5 X = 21

Question 8 Interpreting bifurcation diagram 11 / 14 pts 8.1 Find bifurcations 3 / 4 pts  − 1 pt Bifurcation point at 0.1 incorrect or not listed 8.2 Phase portrait 4 / 4 pts  − 0 pts Correct 8.3 Changing nutrient level 1.5 / 2 pts  − 0.5 pts Answer does not include both 0.05 and 0.85 8.4 Reaching target 2.5 / 4 pts  − 1.5 pts Removal of animal pop not mentioned Question 9 Conceptual questions 8 / 8 pts 9.1 Attractors 4 / 4 pts  − 0 pts Correct 9.2 Vector fields as functions 4 / 4 pts  − 0 pts Correct