called a node. It is asymptotically stable if eigenvalues are both negative, unstable if both are positive values. Classification of various trajectories is descripted in the following table. Eigenvalues Description Behavior Stability b1 b2 real, distinct, node - unstable both positive outgoing real, distinct, saddle unstable opposite sign real, distinct, node- ingoing stable both negative real, repeated node - unstable positive degenerate real, repeated, node - stable negative degenerate complex, spiral - unstable positive real outgoing part complex, spiral -ingoing stable negative real part complex - pure center stable imaginary ellipse
called a node. It is asymptotically stable if eigenvalues are both negative, unstable if both are positive values. Classification of various trajectories is descripted in the following table. Eigenvalues b1 b2 Description Behavior Stability real, distinct, both positive node - outgoing unstable real, distinct, opposite sign saddle unstable real, distinct, both negative node- ingoing stable real, repeated positive node - degenerate unstable real, repeated, negative node - degenerate stable complex, positive real part spiral - outgoing unstable complex, negative real part spiral -ingoing stable complex - pure imaginary center ellipse stable
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