Consider the system of equations dx dt = x(1-x 2-y) dy dt =

Last updated: 7/21/2022

Consider the system of equations dx dt = x(1-x 2-y) dy dt = y(1-y 3-x), taking (x, y) > 0. (a) 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: (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 2,3 2). trajectories ? the point (Enter the point as an (x,y) pair, e.g., (1,2).)