10 terms

Evals: distinct+positive+real

Crit Point Type?

Stability?

Crit Point Type?

Stability?

Nodal Source

Unstable

Unstable

Evals: distinct+negative+real

Crit Point Type?

Stability?

Crit Point Type?

Stability?

Nodal Sink

Asymptotically stable

Asymptotically stable

Evals: distinct+1 negative, 1 positive+real

Crit Point Type?

Stability?

Crit Point Type?

Stability?

(0,0) is a saddle

Unstable

Unstable

Evals: distinct+complex, with negative real part

Crit Point Type?

Stability?

Crit Point Type?

Stability?

(0,0) is a spiral point

Asymptotically stable (spiral sink)

Asymptotically stable (spiral sink)

Evals: distinct+complex, with positive real part

Crit Point Type?

Stability?

Crit Point Type?

Stability?

(0,0) is a spiral point

Unstable (spiral source)

Unstable (spiral source)

Evals: distinct+complex, with zero real part

Crit Point Type?

Stability?

Crit Point Type?

Stability?

(0,0) is a spiral point

Stable (center)

Stable (center)

Evals: repeated+positive+real WITH DIAGONAL MATRIX

Crit Point Type?

Stability?

Crit Point Type?

Stability?

(0,0) is unstable proper node (star node)

Unstable

Unstable

Evals: repeated+negative+real WITH DIAGONAL MATRIX

Crit Point Type?

Stability?

Crit Point Type?

Stability?

(0,0) is stable proper node (star node)

Asymptotically stable

Asymptotically stable

Evals: repeated+positive+real NOT DIAGONAL

Crit Point Type?

Stability?

Crit Point Type?

Stability?

Improper node (degenerative node)

Unstable

Unstable

Evals: repeated+negative+real NOT DIAGONAL

Crit Point Type?

Stability?

Crit Point Type?

Stability?

Improper node (degenerative node)

Asymptotically stable

Asymptotically stable