# 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
.

## Question #1

- 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

Previous: Introduction

Frederick J. Wicklin <fjw@geom.umn.edu>
Brian Burt<burt@geom.umn.edu>
Document Created: Wed Jan 25 CST

Last modified: Tue Mar 14 10:27:19 1995