---
tag: 0F2SYCKDT2
kind: concept
name: Lyapunov stability
msc: [34D20]
sources:
  - url: https://en.wikipedia.org/wiki/Lyapunov_stability
    locator: lead section
same_as:
  wikidata: Q1341651
  wikipedia: Lyapunov stability
---

## Summary

An equilibrium point of a dynamical system is Lyapunov stable if all solutions that start near it stay near it for all future time.
The theory goes back to Aleksandr Lyapunov. See the [[definition|092S6VBECQ]] and the stronger notion of [[asymptotic stability|05Y1JAM3Y5]].