- #1

Niles

- 1,866

- 0

## Homework Statement

Hi all.

I am given by following linear system:

[tex]

\begin{array}{l}

\dot x = dx/dt = ax \\

\dot y = dy/dt = - y \\

\end{array}

[/tex]

The eigenvalue of the matrix of this system determines the stability of the fixpoint (0,0):

[tex]

A=\left( {\begin{array}{*{20}c}

a & 0 \\

0 & { - 1} \\

\end{array}} \right) \quad \Rightarrow \quad \lambda_{1,2}= 0, a.

[/tex]

So there are two eigenvalues given by 0 and

*a*. When a<0, both eigensolutions decay, and the fixpoint (0,0) is

**stable**. When a>0, we have a saddle point.

But what happens when a=0? How can I determine the stability there?

Thanks in advance.Niles.