MATH MODELING(NEED THE CODE)

In this lab you will explore the Lotka-Volterra model of competition between two species. Suppose that rabbits and sheep compete for the same food supply (grass) and the amount available is limited. Let x(t) be the population of rabbits and y(t) be the population of sheep, where x, y 0. For each of the models given below: (a) Plot the nullclines (b) Determine the number of fixed points (c) Determine the type and stability of each fixed point (d) Draw a phase portrait, showing trajectories starting from enough different initial conditions to demonstrate all the qualitatively different solutions (e) Provide a brief biological interpretation of the solutions

1. dx /dt = x(3 x 2y)

dy /dt = y(2 x y)

2. dx /dt = x(3 x y)

dy /dt = y(2 x y)

3. dx /dt = x(3 2x y)

dy /dt = y(2 x y)

4. dx/dt = x(3 2x 2y)

dy /dt = y(2 x y)