Toronto Math Forum

MAT244--2018F => MAT244--Lectures & Home Assignments => Topic started by: Qingyang Wei on December 06, 2018, 01:44:44 PM

Title: How to draw phase portraits by hand effectively?
Post by: Qingyang Wei 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?

Title: Re: How to draw phase portraits by hand effectively?
Post by: Karim El Komaishy 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

Title: Re: How to draw phase portraits by hand effectively?
Post by: Ruowen Xia 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

Title: Re: How to draw phase portraits by hand effectively?
Post by: Zhihao Zuo 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.