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Consider the system of equations da = x(3 – x – 4y) dt dy = y(1 – 3æ), dt taking (x, y) > 0. 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 horizontal nullcline of this system is a line on which = 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 (4, 2), trajectories ? v the point (Enter the point as an (x,y) pair, e.g., (1,2).)

Consider the system of equations da = x(3 – x – 4y) dt dy = y(1 – 3æ), dt taking (x, y) > 0. 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 horizontal nullcline of this system is a line on which = 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 (4, 2), trajectories ? v the point (Enter the point as an (x,y) pair, e.g., (1,2).)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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Consider the system of equations dx = x(3 – x – 4y) dt dy = y(1 – 32), dt taking (x, y) > 0. 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 horizontal nullcline of this system is a line on which = 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 (4, 2), trajectories ? v the point (Enter the point as an (x,y) pair, e.g., (1,2).)
Transcribed Image Text:Consider the system of equations dx = x(3 – x – 4y) dt dy = y(1 – 32), dt taking (x, y) > 0. 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 horizontal nullcline of this system is a line on which = 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 (4, 2), trajectories ? v the point (Enter the point as an (x,y) pair, e.g., (1,2).)
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