| Equilibrium point | Eigenvalue | Case | Sign of the eigenvalue | Nature of the point |
|
|
| Case I |
| Stable |
| Case II | Both | Stable | ||
| Case III |
| Unstable | ||
|
|
| Case I |
| Stable |
| Case II | Both the eigenvalues | Stable | ||
| Case III |
| Unstable |
is zero and 
is negative
and 
are negative
is positive and 
is negative
is negative while 
is zero
and 
are negative
is negative while 
is positive