LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTA== QyQtSSV3aXRoRzYiNiNJJnBsb3RzRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlISIi QyQtSSV3aXRoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJKERFdG9vbHNHRiUhIiI= Plotting phase portraits Here is a sample showing one orbit: 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 Notice the 'jaggies'. To smooth out the curve, increase the number of points being used by the numerical solver, using the option numpoints. 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You can plot more than one orbit by giving other sets of initial conditions: 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To extend the orbits further forward or backward in time, change the time interval on t : 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Notice that, because we did not specify a window, Maple is choosing an asymmetric plot window, just to fit the extent of the specified orbits. This distorts the actual slopes along the orbits. You can specify the window to correct this, and then adjust the t interval until the orbits go to the edges of the window. 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Choosing a suitable set of initial conditions is a bit of an art, as you also don't want the diagram to become too cluttered. I usually start by just choosing a few points around the perimeter of the window, and then adapting the t interval to ensure the orbits go to the edge of the window. The orbits here are asymptotically stable, so they move towards 0 as t increases; if they were unstable, you'd need more negative t values. Just play with initial values and t intervals until you get a nice looking portrait. (This one took me about five tries.) 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Here's a sample plot of some concentric circles. LUktaW1wbGljaXRwbG90RzYiNiY8JS8sJiokSSJ4R0YkIiIjIiIiKiRJInlHRiRGK0YsRiwvRigiIiUvRigiIiovRio7JCEjTiEiIiQiI05GNy9GLkY0L0krZ3JpZHJlZmluZUdGJEYr

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