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Cl *L @\" {curse MATH 146 WiZO 7 C l '3 Summary sheet 7 Lecture 1( l '3 Summary sheet 7 Lecture 1t] 7:; Crowdmark X In Homework Help 7 QSLA fror + V X e 9 O Q El https://app,crowdmarkcom/student/assessments/assignment-week-to-crowdmark ' if {a L l? 6 Q1 (10 points) We consider the effects of shing on a fish population. Let N(t) be the sh population as a function of time. We consider the logistic growth model with saturated harvesting, for which the rate of change of the fish population satises: dN N N 7 N 1 H dt T ( K) A+N' for some constants r, K, H and A. Let's x r : 110 and K : 1000 as before. The sh catch term can be understood as follows: H is the maximum catch rate (the catch rate when N ) 00), and A is the size of the population for which the catch rate is exactly half the maximum catch rate. As the population increases, the sh catch rate increases, but it is bounded above by the max catch rate H. This is realistic; the more fish there is, the easier it is to catch them, but in real life there's also a limit to the number of sh that can be caught, due to limited number of fishermen, boats, etc. (a) Do a phase line analysis for the case with H : 20 and A : 200. What are the equilibrium solutions? Are they stable or unstable? What will happen to the sh population in the long run? (b) Do a phase line analysis for the case with H = 20 and A = 50. What are the equilibrium solutions? Are they stable or unstable? What will happen to the sh population in the long run? (c) In the latter case, you should have found a threshold population below which the population cannot sustain itself and goes extinct. This is somewhat similar to the logistic growth model with constant harvesting that we studied in class. Can you explain what is the main difference in the extinction scenario between these two models? + Drag and drop your images or click to browse... 18:20 2020/3/17 E