Question

(1 point) Consider the system of equations $frac{dx}{dt} = x(1 - frac{x}{5} - y)$ $frac{dy}{dt} = y(1 - frac{y}{6} - x)$, 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 $(frac{1}{2}, frac{6}{5})$, trajectories converge to the point (Enter the point as an $(x, y)$ pair, e.g., $(1, 2)$.)

          (1 point) Consider the system of equations
$frac{dx}{dt} = x(1 - frac{x}{5} - y)$
$frac{dy}{dt} = y(1 - frac{y}{6} - x)$, 
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 $(frac{1}{2}, frac{6}{5})$, trajectories converge to the point
(Enter the point as an $(x, y)$ pair, e.g., $(1, 2)$.)

$(1 point) Consider the system of equations fracdxdt = x(1 - fracx5 - y) fracdydt = y(1 - fracy6 - x), taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: (Enter your equation, e.g., y = x.) And for the (non-zero) horizontal (y-)nullcline: (Enter your equation, e.g., y = x.) (Note that there are also nullclines lying along the axes.) (b) What are the equilibrium points for the system? Equilibria = (Enter the points as comma-separated (x, y) pairs, e.g., (1, 2), (3, 4).) (c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence: If we start at the initial position (frac12, frac65), trajectories converge to the point (Enter the point as an (x, y) pair, e.g., (1, 2).)$

Added by Eric C.

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