Asymptotically stability

  1. 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.
     
  2. jcsd
  3. This can be evaluated by considering real part of eigenvalues < 0.

    But can you let me visualize it conceptually?
     
  4. Moreover, will a "center" be referred to as a stable or unstable equilibrium?
     
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