Consider the system of equationsdx dt = x(1-x 2-y)dy dt = y(1-y 3-x),taking (x, y)...

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Calculus

Consider the system of equationsdx 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).)

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Consider the system of equationsdx 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).)