Divergence at a Point
In this lab we will consider the vector field given by the equations:
dx/dt = y
dy/dt = -x^3 + x + (3/2)x^2 + y - x^2*y
The phase portrait of this vector field looks like Figure 1.
Figure 1: Phase portrait and equilibria.
Let f denote the right-hand side of this system,
f(x,y)=(y, -x^3 + x + (3/2)x^2 + y - x^2*y),
and recall that
- Compute the location of equilibria for this vector field.
- Compute div(f).
- Evaluate div(f) at each equilibrium.
- Based on the previous computation, what do you think is the stability
type of each equilibrium? How confident are you?
Next: Divergence over a Region
Frederick J. Wicklin <firstname.lastname@example.org>
Document Created: Wed Jan 25 CST
Last modified: Tue Mar 14 10:27:19 1995