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

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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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Consider the system of equations dæ = x(3 – x – 4y) dt dy = y(1 – 32), dt taking (x, y) > 0. Recall that nullcline of this system is a line on which de = 4 = 0. Likewise, a vertical nullcline of this system is a line on which de = 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, 1), trajectories ? v the point (Enter the point as an (x,y) pair, e.g., (1,2).)
Transcribed Image Text:Consider the system of equations dæ = x(3 – x – 4y) dt dy = y(1 – 32), dt taking (x, y) > 0. Recall that nullcline of this system is a line on which de = 4 = 0. Likewise, a vertical nullcline of this system is a line on which de = 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, 1), trajectories ? v the point (Enter the point as an (x,y) pair, e.g., (1,2).)
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