# Predator Prey Question

• Jan 11th 2009, 06:12 AM
stardust
Predator Prey Question
Actually I know almost nothing about how to write the codes in Matlab but I have to solve this question to pass my course.How can i solve this question

The populations of Canis lupus (wolves) and Rangifer tarandus (reindeer)
in the environment can be described by the system of differential equations
(
X′(t) = X(t)(a − bY (t))
Y ′(t) = Y (t)(cX(t) − d),
(1)
where X(t) is the population of Rangifer tarandus and Y (t) is the population
of Canis lupus. The constants are a = 8, b = .25, c = .02 and
d = 10 and the initial populations are X(0) = 600 and Y (0) = 60. Using
the MATLAB code ode45 solve (1) for 0 <= T<= 2 and plot X(t) and Y(t)
• Jan 11th 2009, 10:26 AM
Constatine11
Quote:

Originally Posted by stardust
Actually I know almost nothing about how to write the codes in Matlab but I have to solve this question to pass my course.How can i solve this question

The populations of Canis lupus (wolves) and Rangifer tarandus (reindeer)
in the environment can be described by the system of differential equations
(
X′(t) = X(t)(a − bY (t))
Y ′(t) = Y (t)(cX(t) − d),
(1)
where X(t) is the population of Rangifer tarandus and Y (t) is the population
of Canis lupus. The constants are a = 8, b = .25, c = .02 and
d = 10 and the initial populations are X(0) = 600 and Y (0) = 60. Using
the MATLAB code ode45 solve (1) for 0 <= T<= 2 and plot X(t) and Y(t)

You define a state vector:

$\displaystyle \mathbf{X}=\left[ \begin{array}{c} x\\ y \end{array} \right]$

Then:

$\displaystyle \mathbf{X}'=\left[ \begin{array}{c} \mathbf{X}_1(a-b\mathbf{X}_3)\\ \mathbf{X}_2(c\mathbf{X}_1-d)\\ \end{array} \right]$