2. Consider the following dynamical system on the plane: x = (x-3)(y-2), y = yx²-x. X. (a) Determine the location of the equilibrium points and use linear stability analysis to classify them. When the eigenvalues are real, compute the eigenvectors. (b) Sketch the phase portrait of the system - this must include: equilibria, local behaviour at the equilibria, isoclines and global behaviour.
2. Consider the following dynamical system on the plane: x = (x-3)(y-2), y = yx²-x. X. (a) Determine the location of the equilibrium points and use linear stability analysis to classify them. When the eigenvalues are real, compute the eigenvectors. (b) Sketch the phase portrait of the system - this must include: equilibria, local behaviour at the equilibria, isoclines and global behaviour.
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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Transcribed Image Text:2. Consider the following dynamical system on the plane:
x = (x-3)(y-2),
y = yx²-x.
X.
(a) Determine the location of the equilibrium points and use linear stability analysis to classify
them. When the eigenvalues are real, compute the eigenvectors.
(b) Sketch the phase portrait of the system - this must include: equilibria, local behaviour at the
equilibria, isoclines and global behaviour.
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