Four nonlinear models are described below. For each one: a. Use the x\' and y\'

Question

Four nonlinear models are described below. For each one:
a. Use the x' and y' nullclines to find all of the equilibrium points in the given region of the phase plane.
b. Compute the Jacobian matrix of the system.
c. Determine the type of each equilibrium point (if possible).
d. Use the information from part c to sketch a phase portrait by hand. Show as much detail as you can.
e. Use technology to draw a phase portrait, and compare it to your sketch from part d. Plot enough solution curves to determine the behavior of solutions everywhere in the specified region of the phase plane. Use whatever technology you have available.

1. Competing species model. The functions x(t) and y(t) represent the population size, at time t, of two competing species in the same ecosystem. Their growth equations are given by x’= x(1 - x) - xy, y’= y(3/4- y) - 1/2 xy.
Let x vary between 0 and 1.5, and y between 0 and 1.5

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Hello! Could you please give me the points? I really need them... please? :(

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