Stability Classification: How to Determine if a System is Asymptotically Stable?

[ceomtcl]

Homework Statement

How can i classify

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

as either

(a) stable or asymptotically stable?

Homework Equations

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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?