10 terms

Phase Portrait Reference Guide

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Evals: distinct+positive+real
Crit Point Type?
Stability?
Nodal Source
Unstable
Evals: distinct+negative+real
Crit Point Type?
Stability?
Nodal Sink
Asymptotically stable
Evals: distinct+1 negative, 1 positive+real
Crit Point Type?
Stability?
(0,0) is a saddle
Unstable
Evals: distinct+complex, with negative real part
Crit Point Type?
Stability?
(0,0) is a spiral point
Asymptotically stable (spiral sink)
Evals: distinct+complex, with positive real part
Crit Point Type?
Stability?
(0,0) is a spiral point
Unstable (spiral source)
Evals: distinct+complex, with zero real part
Crit Point Type?
Stability?
(0,0) is a spiral point
Stable (center)
Evals: repeated+positive+real WITH DIAGONAL MATRIX
Crit Point Type?
Stability?
(0,0) is unstable proper node (star node)
Unstable
Evals: repeated+negative+real WITH DIAGONAL MATRIX
Crit Point Type?
Stability?
(0,0) is stable proper node (star node)
Asymptotically stable
Evals: repeated+positive+real NOT DIAGONAL
Crit Point Type?
Stability?
Improper node (degenerative node)
Unstable
Evals: repeated+negative+real NOT DIAGONAL
Crit Point Type?
Stability?
Improper node (degenerative node)
Asymptotically stable