Letting , we see that the stability of an autonomous system is related to that of the simple linear IVP
(1.11)
Its solution is given by
and hence, (1.11) is
stable when ,
asymptotically stable when and
unstable when
Remark: These conclusions remain true for the original non linear autonomous problem when and y is small enough for the term to be negligible relative to . This cannot happen in the stable case hence, it requires a more careful analysis.
, we see that the stability of an autonomous system is related to that of the simple linear IVP 
, 
and 
and y is small enough for the 
term to be negligible relative to 
. This cannot happen in the stable case 
hence, it requires a more careful analysis. 
