- #1

- 97

- 0

## Homework Statement

Find all critical points and derive the linearised system about each critical point

[itex]\dot{y}[/itex] = [3y

_{1}+ y

_{1}y

_{2}; y

_{1}+ y

_{2}- y

_{2}

^{2}]

## Homework Equations

## The Attempt at a Solution

Setting

0 = 3y

_{1}+ y

_{1}y

_{2}so y

_{2}= -3

0 = y

_{1}+ y

_{2}- y

_{2}

^{2}so y

_{1}= 12

= [0, 1; 12, -3]

so p = -3 (<0)

q = -12 (<0)

[itex]\Delta[/itex] = 57 (>0)

Is this right that my only critical point is (12,-3) and is that how I determine the nature of the critical point and whether my critical point is stable or unstable with my values for p, q and [itex]\Delta[/itex]?