. 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?