The stability of the Equilibrium Point 0

Published On :2021-02-12 23:40:00

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Let  A a 2*2 Matrix .
  1.  If all the eigenvalues of  A have negative real part , then 0 is sink (asymptotical stable ) .
  2. If all the eigenvalues of A have positive real part , then 0 is source (unstable) .
  3. If  A has at least one eigenvalues with positive real part and at least one eigenvalues with negative real part and and none of the eigenvalues has a zero real part , then 0 is saddle (unstable ).
  4. If all the eigenvalues of A have zero real parts then 0 is center (stable but not asymptotical stable ) .