Question

Consider the system of equations dxdt=x(3−x−4y) dydt=y(1−3x), taking (x,y)>0.

(1 point) Consider the system of equations de = 2(3 – 2 – 49) = y(1 - 33), taking (2,y) > 0. (a) Write an equation for the (non-zero) vertical (-)nullcline of this system: (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (y-)nullcline: (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 = (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 (1/3,1), trajectories ? the point (Enter the point as an (x,y) pair, e.g., (1,2).)

Answer 1

Consider the system of equations dxdt=x(3−x−4y) dydt=y(1−3x), taking (x,y)>0.
Answer = 2(3-2-48) da e (1-3x) dt I cal vertical Lenes nullelines a 13-8-44) = 0 X=0 Ori 3-2-4y=0 =) -48=8-3 y = 3-x Horizontal nullelines: G=(1-3x)=0 yao on 1-3450 =)bxolle

- (b) Equinbrom points are (0,0), (''3, 3/3), (0,32, 60,314),("3, 0) a . E * F col chios L we If we start at the initial position (4,2) trajectories converge to the point (3,813) -