Consider the system of equations dx/dt = x (1 - x/3 - y) dy/dt = y (1 - y/4 - x)

Question

Consider the system of equations dx/dt = x (1 - x/3 - y) dy/dt = y (1 - y/4 - x), taking (x, y) > 0. Write an equation for the (non-zero) vertical (x-)nullcline of this system: (Enter your equation, e.g., y-x.) And for the (non-zero) horizontal (y-)nullcline: What are the equilibrium points for the system? (Enter the points as comma-separated (x, y) pairs, e.g., (1, 2), (3, 4).) 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). (Enter the point as an (x, y) pair, e.g., (1, 2).)

Explanation / Answer

a)x(1-x/3-y) =0

or x= 0 , 3-x-3y =0

y = -x/3 + 1

b)y(1-y/4 -x) = 0

y= 0 , 4 -y-4x =0

y = -4x+4

c) equilibrium point

y = -x/3 + 1

and y = -4x+4

x= 9/11 ,y = 8/11

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---