Need this done as best you can by 11pm UK GMT tonight (IN 4 HOURS TIME)
Let us now consider x as the number of preys (e.g., gazelles) and y the number of
predators (lions). In the savanna there is plenty of grass, so as long as they do not meet
lions, gazelles reproduce happily
dt = αx, (10)
α > 0. On the other hand, if they do not meet gazelles, lions starve to death
dt = −γy, (11)
γ > 0. But lions and gazelles do meet, and the dynamics of their populations is given
(or better modelled) by the Lotka-Volterra equation
dt = αx − βxy
dt = −γy + δxy . (12)
Write (12) as a vector equation
dt = F(x), (13)
i.e. explicitly write the functional dependence of the components Fi on the components
Plot the vector field F (defined in problem 3.1) on the first quadrant (0 ≤ x ≤ 3000, 0 ≤
y ≤ 300).
Let us now set α = 0.1, β = 10−3
, γ = 0.1 and δ = 10−4 Use MATLAB’s numerical
integrator ODE45 to solve eq. (12) between t = 0 and t = 500. For each initial condition,
plot your results in two different graphs, one showing x and y as functions of time, and
one showing y as a function of x. As initial conditions, use:
x0 = 2000, y0 = 40,
x0 = 3000, y0 = 20,
x0 = 1000, y0 = 100.
Explain (using an equation) what is special about the latter initial conditions.
I have some good experience in MATLAB projects. Did my final year engineering project in MATLAB on stock market analysis. Can send you the project as well. My amount can be negotiated.
3 freelance font une offre moyenne de $127 pour ce travail
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