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Consider the following system of equations dx dt = x(3- 3x - y), dy dt y(3x-3y), for 0≤ x ≤2, 0 ≤ y ≤2. 4 (a) Find all the fixed points of this system. (b) Compute the Jacobian matrix of (4) and determine the linearisation about each fixed point. Calculate the eigenvalues and eigenvectors and hence classify the type and stability of each fixed point, sketching the phase portrait of each linearised system. = = = x are invariant, with respect to 4 (c) Show that the lines x 0, y O and y (d) Sketch a phase portrait of the nonlinear system 4 indicating fixed points, invari- ant lines and the qualitative behaviour.

Consider the following system of equations dx dt = x(3- 3x - y), dy dt y(3x-3y), for 0≤ x ≤2, 0 ≤ y ≤2. 4 (a) Find all the fixed points of this system. (b) Compute the Jacobian matrix of (4) and determine the linearisation about each fixed point. Calculate the eigenvalues and eigenvectors and hence classify the type and stability of each fixed point, sketching the phase portrait of each linearised system. = = = x are invariant, with respect to 4 (c) Show that the lines x 0, y O and y (d) Sketch a phase portrait of the nonlinear system 4 indicating fixed points, invari- ant lines and the qualitative behaviour.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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can you please do c and d

Consider the following system of equations dx dt = x(3- 3x - y), dy dt y(3x-3y), for 0≤ x ≤2, 0 ≤ y ≤2. 4 (a) Find all the fixed points of this system. (b) Compute the Jacobian matrix of (4) and determine the linearisation about each fixed point. Calculate the eigenvalues and eigenvectors and hence classify the type and stability of each fixed point, sketching the phase portrait of each linearised system. = = = x are invariant, with respect to 4 (c) Show that the lines x 0, y O and y (d) Sketch a phase portrait of the nonlinear system 4 indicating fixed points, invari- ant lines and the qualitative behaviour.
Transcribed Image Text:Consider the following system of equations dx dt = x(3- 3x - y), dy dt y(3x-3y), for 0≤ x ≤2, 0 ≤ y ≤2. 4 (a) Find all the fixed points of this system. (b) Compute the Jacobian matrix of (4) and determine the linearisation about each fixed point. Calculate the eigenvalues and eigenvectors and hence classify the type and stability of each fixed point, sketching the phase portrait of each linearised system. = = = x are invariant, with respect to 4 (c) Show that the lines x 0, y O and y (d) Sketch a phase portrait of the nonlinear system 4 indicating fixed points, invari- ant lines and the qualitative behaviour.
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