Consider the system of equations (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.) dx dt (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).) = x(2 - x - 3y) taking (x, y) > 0. dt dt dt. Recall that a nullcline of this system is a line on which = = 0. Likewise, a vertical nullcline of this system is a line on which = 0, and a dy horizontal nullcline of this system is a line on which = 0. dt (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: dy dt = y(1-2x), (c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence: If we start at the initial position (1/2,), trajectories ? ✓the point (Enter the point as an (x,y) pair, e.g., (1,2).)

Consider the system of equations (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.) dx dt (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).) = x(2 - x - 3y) taking (x, y) > 0. dt dt dt. Recall that a nullcline of this system is a line on which = = 0. Likewise, a vertical nullcline of this system is a line on which = 0, and a dy horizontal nullcline of this system is a line on which = 0. dt (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: dy dt = y(1-2x), (c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence: If we start at the initial position (1/2,), trajectories ? ✓the point (Enter the point as an (x,y) pair, e.g., (1,2).)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Systems Of Linear Equations

Section1.1: Introduction To Systems Of Linear Equations

Problem 72E: Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by...

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Question

Consider the system of equations
(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.)
dx
dt
(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).)
= x(2 - x - 3y)
taking (x, y) > 0.
dt
dt
dt.
Recall that a nullcline of this system is a line on which = = 0. Likewise, a vertical nullcline of this system is a line on which = 0, and a
dy
horizontal nullcline of this system is a line on which = 0.
dt
(a) Write an equation for the (non-zero) vertical (x-)nullcline of this system:
dy
dt
= y(1-2x),
(c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence:
If we start at the initial position (1/2,), trajectories ?
✓the point
(Enter the point as an (x,y) pair, e.g., (1,2).)

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