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).)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.1: Introduction To Systems Of Linear Equations
Problem 72E: Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by...
Related questions
Question
100%
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).)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
