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dx = X dt dy = y dt -지). taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: y=1-x/3 (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (y-)nullcline: y=4(1-x) (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 (0, 0), (0, 4), (9/11, 8/11), (3, 0) (Enter the points as comma-separated (x,y) pairs, e.g., (1,2), (3,4),)

dx = X dt dy = y dt -지). taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: y=1-x/3 (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (y-)nullcline: y=4(1-x) (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 (0, 0), (0, 4), (9/11, 8/11), (3, 0) (Enter the points as comma-separated (x,y) pairs, e.g., (1,2), (3,4),)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the System of Equations

* - dx = X dt * (1 --) * =(1--). dy y dt taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: y=1-x/3 (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (y-)nullcline: y=4(1-x) (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 = (0, 0), (0, 4), (9/11, 8/11), (3, 0) %3D (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 (5, ), trajectories converge to the point (1/4,-2/9) (Enter the point as an (x,y) pair, e.g., (1,2).)
Transcribed Image Text:* - dx = X dt * (1 --) * =(1--). dy y dt taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: y=1-x/3 (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (y-)nullcline: y=4(1-x) (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 = (0, 0), (0, 4), (9/11, 8/11), (3, 0) %3D (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 (5, ), trajectories converge to the point (1/4,-2/9) (Enter the point as an (x,y) pair, e.g., (1,2).)
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