(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 anda. When a<0, both eigensolutions decay, and the fixpoint (0,0) isstable. When a>0, we have a saddle point.

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

Thanks in advance.

Best regards,

Niles.

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# Linear Systems of ODE's: Eigenvalues and Stability

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