# Lyapunov stable

A fixed point^{} ${x}^{*}$ is Lyapunov stable^{} if trajectories of nearby points $x$ remain close for future time. More formally the fixed point ${x}^{*}$ is Lyapunov stable, if for any $\u03f5>0$, there is a $\delta >0$ such that for all $t\ge 0$ and for all $x\ne {x}^{*}$ it is verified

$$ |

In particular, $d({x}^{*},x(0))=0$.

Title | Lyapunov stable |

Canonical name | LyapunovStable |

Date of creation | 2013-03-22 13:06:29 |

Last modified on | 2013-03-22 13:06:29 |

Owner | armbrusterb (897) |

Last modified by | armbrusterb (897) |

Numerical id | 10 |

Author | armbrusterb (897) |

Entry type | Definition |

Classification | msc 34D20 |

Synonym | Lyapunov stability |

Synonym | Liapunov stable |

Synonym | Liapunov stability |

Related topic | AsymptoticallyStable |

Related topic | AttractingFixedPoint |

Related topic | StableFixedPoint |

Related topic | NeutrallyStableFixedPoint |

Related topic | UnstableFixedPoint |