- #1
sid9221
- 111
- 0
So I want to be able to draw the phase portrait for linear systems such as:
x'=x-2y
y'=3x-4y
I am completely confused, but this is what I have come up with so far:
Step 1: Write out the system in the form of a matrix.
Step 2: Find the eigenvalues and eigenvectors for the matrix.
Step 3: Using the eigenvectors draw the eigenlines.
Step 4: Using the the eigenvalues label the direction of the eigenlines[(+) = away, (-)= towards]
Step 5: Using the eigenvalues determine the type of the system. Eg: node, star, spiral etc.
Step 6: Fill in a few trajectories.
My issues appear at steps 5 and 6, I can't figure out how to draw the trajectories. Which eigenline should they be based around ?
Also with complex eigenvalues or when there is 1 eigenvector what do I have to do ?
Any help or link to a webpage would be greatly appreciated.
x'=x-2y
y'=3x-4y
I am completely confused, but this is what I have come up with so far:
Step 1: Write out the system in the form of a matrix.
Step 2: Find the eigenvalues and eigenvectors for the matrix.
Step 3: Using the eigenvectors draw the eigenlines.
Step 4: Using the the eigenvalues label the direction of the eigenlines[(+) = away, (-)= towards]
Step 5: Using the eigenvalues determine the type of the system. Eg: node, star, spiral etc.
Step 6: Fill in a few trajectories.
My issues appear at steps 5 and 6, I can't figure out how to draw the trajectories. Which eigenline should they be based around ?
Also with complex eigenvalues or when there is 1 eigenvector what do I have to do ?
Any help or link to a webpage would be greatly appreciated.