# MATLAQ JOB TONIGHT. QUICK ONE! NEEDED IN 4 HOURS TIME

\$50

Need this done as best you can by 11pm UK GMT tonight (IN 4 HOURS TIME)

3 Exercise

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

dx

dt = αx, (10)

α > 0. On the other hand, if they do not meet gazelles, lions starve to death

dy

dt = −γy, (11)

4

γ > 0. But lions and gazelles do meet, and the dynamics of their populations is given

(or better modelled) by the Lotka-Volterra equation

 dx

dt = αx − βxy

dy

dt = −γy + δxy . (12)

3.1 Problem

Write (12) as a vector equation

dx

dt = F(x), (13)

i.e. explicitly write the functional dependence of the components Fi on the components

xi

.

3.2 Problem

Plot the vector field F (defined in problem 3.1) on the first quadrant (0 ≤ x ≤ 3000, 0 ≤

y ≤ 300).

3.3

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:

3.4 Problem

x0 = 2000, y0 = 40,

3.5 Problem

x0 = 3000, y0 = 20,

3.6 Problem

x0 = 1000, y0 = 100.

3.7 Problem

Explain (using an equation) what is special about the latter initial conditions.

Concernant l'employeur :
( 46 commentaires ) Kingston Upon Thames, United Kingdom

Nº du projet : #10190949

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