Asymptotically stability

ceomtcl

1. The problem statement, all variables and given/known data

How can i classify

(1) stable node
(2) saddle and
(3) center

as either

(a) stable or asymptotically stable?

2. Relevant equations

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3. The attempt at a solution

All three are stable. Stable node seems to be asymptotically stable. But I am not sure about Saddle and center? I think saddle is not asymptotically stable.

ceomtcl

This can be evaluated by considering real part of eigenvalues < 0.

But can you let me visualize it conceptually?

ceomtcl

Moreover, will a "center" be referred to as a stable or unstable equilibrium?