### Author Topic: How to draw phase portraits by hand effectively?  (Read 2009 times)

#### Qingyang Wei

• Jr. Member
• Posts: 6
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##### How to draw phase portraits by hand effectively?
« on: December 06, 2018, 01:44:44 PM »
The only method of drawing phase portrait that I am aware of is to evaluate each particular solutions of the system at a large amount of points, and "connect the dots" to produce a trajectory for the solution. But that seems to be very time consuming. Is there any more efficient way to draw this by hand?

#### Karim El Komaishy

• Newbie
• Posts: 3
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##### Re: How to draw phase portraits by hand effectively?
« Reply #1 on: December 06, 2018, 04:30:48 PM »
Try finding the eigenvectors as well as the eigenvalues as the eigenvectors can tell you the direction of the trajectories

#### Ruowen Xia

• Newbie
• Posts: 2
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##### Re: How to draw phase portraits by hand effectively?
« Reply #2 on: December 09, 2018, 02:26:24 PM »
You can divided into different situations, like 2 distinct real roots, 2 same real roots and non-real roots. and fine the corresponding eigenvector, and first draw these eigenvectors

#### Zhihao Zuo

• Jr. Member
• Posts: 5
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##### Re: How to draw phase portraits by hand effectively?
« Reply #3 on: December 11, 2018, 10:48:57 AM »
I got the same question. And sometimes I just couldn't connect all the lines together however hard I try.