Consider the system of equations:
dx/dt = x(1 - x/3 - y)
dy/dt = y(1 - y/4 - x)
taking (x,y) > 0.
(a) Write an equation for the (non-zero) vertical (x-)nullcline of this system:
(x/3)+y=1
(Enter your equation, e.g., y=x.)
And for the (non-zero) horizontal (y-)nullcline:
x+(y/4)=1
(Enter your equation, e.g., y=x.)
(Note that there are also nullclines lying along the axes.)
(b) What are the equilibrium points for the system?
Equilibria = (9/11,8/11),(0,0),(0,4),(3,0)
(Enter the points as comma-separated (x,y) pairs, e.g., (1,2), (3,4).)
(c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence:
If we start at the initial position (1/2, 4/3), trajectories converge to the point
(2,1/3)
(Enter the point as an (x,y) pair, e.g., (1,2).)