Go with the flow

Two vignettes from Dynamical Systems this semester.

Students were studying for the Dynamical Systems final exam in the department library.   A computer science major strolled by and, seeing the activity, asked “Why is it I always find this room filled with math majors?”   The students looked at each other before one of them, Proper Michael, answered.

“Because this room is a sink,” he said, “and we all get sucked in!”

The other math majors chuckled knowingly, while the CS major rolled his eyes and walked away with a disgusted sigh.

“Oh dear,” said Michael.   “I guess it’s a saddle now.”

One of the questions on the final homework set involved a dynamical system modeling two competing species of animals (in this case, rabbits and woodchucks).   I did get some interesting answers out of that problem.

For example, after doing some basic graphical analysis of the model, the problem asks why it is impossible for the orbits of the dynamical system (that is, the curves modeling the pairs of populations over time) to leave the first quadrant:

Of course, the point of the problem was to show that the two populations would not coexist, since the only co-habitation equilibrium is an unstable saddle point. However, that answer hardly does this one justice:

Click to embiggen, and enjoy.

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