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Asymptotically stability

by ceomtcl
Tags: asymptotically, stability
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ceomtcl
#1
Nov4-08, 01:13 PM
P: 14
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

<None>

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.
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ceomtcl
#2
Nov4-08, 01:17 PM
P: 14
This can be evaluated by considering real part of eigenvalues < 0.

But can you let me visualize it conceptually?
ceomtcl
#3
Nov4-08, 01:21 PM
P: 14
Moreover, will a "center" be referred to as a stable or unstable equilibrium?


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