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Only need the answer of Q8 and Q9


. Interpret physically the form of the harvesting rate in (b) and (c). What does the parameter A
stand for physically. Which model of a harvesting rate do you think is more physical? . Non-dimensionalize the models to obtain the forms
a) Lt=m(1——1:)—-h
b) at=m(1—a:)—hm c)i=x(1~m)—-hfi . For models (a) and (b) find the fixed points and determine their stability for different values of h.
Are any of them unphysical? . (MATLAB) plot the bifurcation diagrams for the cases (a) and (b). Label stable, unstable branches
and bifurcation points. . Do the normal form analysis in the cases (a) and (b) and obtain analytically the results you got
using MATLAB in the item above. For model (c): . Show that the system can have one, two, or three fixed points, depending on the values of a and h.
Classify the stability of the fixed points in each case. . Analyze the dynamics near a: = 0 and show that the bifurcation occurs when h = a. What type of
bifurcation is it? . Show that another bifurcation occurs when in = flu + 1)2, for a < ac, where ac is to be determined.
Classify the bifurcation. . Plot the stability diagram of the system in (0,11) parameter space. (The stability diagrams in 2-
dimensional parameter space will be shown in class on Tuesday). Can hysteresis occur in any of the
stability regions?

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