Every year, in Africa there is a great animal migration. The about two million W

Question

Every year, in Africa there is a great animal migration. The about two million Wildebeest and Zebras move south toward fresh short grasses. https: //isafari.nathab.com/the - great - immigration Clearly the population of Zebra's and Wildebeest are completing for the same food source and co - existing. They actually group together in the open savannah to decrease predation. We model the Wildebeest (w) and Zebra (z) interaction by the simplification: dw/dt = r_1 w (1 - w/K_1 - z/J_2) dz/dt = r_2 z (1 - z/K_2 - w/J_1) which gives the logistic equations if either animal is missing and basically says they somehow share the carrying capacity. Can this model predict long term co - existence? Your first step is to find all the critical points. There are always at least 3: (0, 0) mutual extinction. (K_1, 0) zebra extinction and (0, K_2) wildebeest extinction. Sometimes there are four. You need to classify these with respect to stability. There are nine possible cases that come from the different orderings of J_1 vs K_1 and J_2 vs K_2 your job is completely analyze the critical points and draw the phase diagram (in the first quadrant) of the four of these that are drawn on the next page.

Explanation / Answer

The eqns can be solved using Runge Kutta 4rth order method .

Let dw/dt = f(w,z.t)

dz/dt = g(w,z,t)

k1 = h.f(w0,z0,t0)

l1 = h.g(w0,z0,t0)

k2 = h.f(w0+k1/2,z0+l1/2,t0+h/2)

l2 = h.g(w0+k1/2,z0+l1/2,t0+h/2)

and so on .

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