ALL THE KINDS OF CRITICAL POINTS FOR 2-Dimemnsional Linear Systems of Differential Equations

Case Ia: TWO Real, distinct and both positive eigenvalues

UNSTABLE NODE. The direction is AWAY from the origin.

Case Ib: TWO Real, distinct and both negative eigenvalues

ASYMPTOTICALLY STABLE NODE. The direction is TOWARDS from the origin.

Case Ic: TWO Real, distinct , OPPOSITE SIGNS

UNSTABLE SADDLE POINT. The direction is from (0,-infinity) to (infinity, 0)

Case IIa1: EQUAL POSITIVE EIGENVALUES, EIGENSPACE 2-Dim

UNSTABLE PROPOER NODE. The direction is AWAY from the origin.

Case IIa2: EQUAL POSITIVE EIGENVALUES, EIGENSPACE 1-Dim

UNSTABLE IMPROPOER NODE. The direction is AWAY from the origin.

Case IIb1: EQUAL NEGATIVE EIGENVALUES, EIGENSPACE 2-Dim

ASYMPOTICALLY STABLE PROPOER NODE. The direction is TOWARDS from the origin.

Case IIb2: EQUAL NEGATIVE EIGENVALUES, EIGENSPACE 1-Dim

ASYMPOTICALLY STABLE IMPROPOER NODE. The direction is TOWARDS from the origin.

Case IIIa: COMPLEX EIGENVALUES, POSTIVE REAL PART

UNSTABLE SPIRAL POINT. The direction is AWAY from the origin.

Case IIIb: COMPLEX EIGENVALUES, NEGATIVE REAL PART

ASYMPTOTICALLY STABLE SPIRAL POINT. The direction is TOWARDS from the origin.

Case IIIc: COMPLEX EIGENVALUES, ZERO REAL PART

STABLE CENTER.

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