---
tag: 0AAQ73WRFB
kind: concept
name: Limit cycle
msc: [34C07]
sources:
  - url: https://en.wikipedia.org/wiki/Limit_cycle
    locator: lead section
same_as:
  wikidata: Q1545916
  wikipedia: Limit cycle
---

## Summary

A limit cycle is a closed trajectory of a planar dynamical system with one property. At least one other trajectory spirals into it as time tends to $\infty$ or to $-\infty$.
Limit cycles model oscillations that sustain themselves. See the [[definition|0EERDDPSVT]].

## Remarks

Henri Poincaré started the study of limit cycles.