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Consider the system of equations #--(1--) da dt *= (1 ---). dy dt 3 taking (2, 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 (, ), trajectories converge to v the point (Enter the point as an (x,y) pair, e.g., (1,2).)

Consider the system of equations #--(1--) da dt *= (1 ---). dy dt 3 taking (2, 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 (, ), trajectories converge to v the point (Enter the point as an (x,y) pair, e.g., (1,2).)

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 *--(1 --) * - v(1 --). =>(1 – % - -), da dt dy dt = 11 taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (æ-)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 (, ), trajectories converge to v the point (Enter the point as an (x,y) pair, e.g., (1,2).)
Transcribed Image Text:Consider the system of equations *--(1 --) * - v(1 --). =>(1 – % - -), da dt dy dt = 11 taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (æ-)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 (, ), trajectories converge to v the point (Enter the point as an (x,y) pair, e.g., (1,2).)
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