# System differential equations

## Homework Statement

Determine the equibrilium solutions and their stability properties of the system below:

$$\dot{x} = (1-z)[(4-z^2)(x^2+y^2-2x+y)-4(-2x+y)-4]$$

$$\dot{y} = (1-z)[(4-z^2)(xy-x-zy)-4(-x-zy)-2z]$$

$$\dot{z} = z^2(4-z^2)(x^2+y^2)$$

## The Attempt at a Solution

The critical point (0,0,1) is difficult to characterise since the eigenvalues are 0, 0, 0. However you can determine stabilitity of this point by looking at the flow of z' ... but how?