Lyapunov stability criterion

Let be a Fixed point with neighbourhood of a differential system and let be differentiable with as a minimum in . Denote . Then¹² #m/thm/dynamics/flow

is asymptotically stable if for all
is Lyapunov stable if for all
is Lyapunov unstable if for all
is asymptotically unstable if for all

Proof

#missing/proof

#state/develop | #lang/en | #SemBr

2024. Nonlinear dynamics and chaos: With applications to physics, biology, chemistry, and engineering, §7.2, pp. 224–225 ↩
2021. MATH3021: Nonlinear dynamics & chaos, p. 49 ↩