Please answer all parts of the Mathematical modeling question The following set

Question

Please answer all parts of the Mathematical modeling question

The following set of equations models the populations of rabbits R and wolves W dR/dt = 0.08R(1 - 0.0002R) - 0.001 RW dW/dt = -0.02W + 0.00002 RW (i) According to these equations, what happens to the rabbit population in the absence of wolves? (ii) The figure shows the phase trajectory that starts at the point (1000, 40). Describe what eventually happens to the rabbit and wolf populations. (iii) Sketch graphs of the rabbit and wolf populations as functions of time. Is there a steady state shown in the figure? What is its type?

Explanation / Answer

(a) If W=0

then the rate of change of population of rabbits is negative which means eventually rabbit population will reach zero.

(b) From the phase trajectory, we can see that eventually the population will reach (1000,64) i.e R=1000 and W=64

(c) MATLAB is not able to solve the system of equations.

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