- #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.