Integrating Lotka-Volterra Equations with Known Parameters

[Ry122]

I'm trying to solve these differential equations given the initial conditions 0.5.
http://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equation"
α, β, γ and δ are known.

What's the correct method for doing this? I know how to use the Euler method to integrate a single ODE, but not a system of ODEs like this.

 

[jackmell]

Solve them simultaneously: Compute the first increment for x(t) say. You can do this for an IVP since you know the starting values of x(t) and y(t) as well as their derivatives. So you get the next value, x_1. Now, find y_1 the same way. Now find (x_2, y_2), (x_3,y_3)[/tex] and so on.

 

[Ry122]

what equation do i sub (x2,y2) and (x3, y3) into to get the final coordinate positions?