dx x(3 – z - dt – 4y) dy y(1 – 3x), dt taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: y=(-x/4)+(3/4) (Enter your equation, eg., y=x.) And for the (non-zero) horizontal (y-)nullcline: x=1/3 (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 (1/3, 1), trajectories converge to the point (Enter the point as an (x,y) pair, e.g., (1,2).)

dx x(3 – z - dt – 4y) dy y(1 – 3x), dt taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: y=(-x/4)+(3/4) (Enter your equation, eg., y=x.) And for the (non-zero) horizontal (y-)nullcline: x=1/3 (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 (1/3, 1), trajectories converge to the point (Enter the point as an (x,y) pair, e.g., (1,2).)

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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