# autonomous system

A system of ordinary differential equation is *autonomous ^{}* when it does not depend on time (does not depend on the independent variable) i.e. $\dot{x}=f(x)$. In contrast

*nonautonomous*is when the system of ordinary differential equation does depend on time (does depend on the independent variable) i.e. $\dot{x}=f(x,t)$.

It can be noted that every nonautonomous system can be converted to an autonomous system by adding a dimension. i.e. If $\dot{\text{\mathbf{x}}}=\text{\mathbf{f}}(\text{\mathbf{x}},t)$ $\text{\mathbf{x}}\in {\mathbb{R}}^{n}$ then it can be written as an autonomous system with $\text{\mathbf{x}}\in {\mathbb{R}}^{n+1}$ and by doing a substitution with ${x}_{n+1}=t$ and ${\dot{x}}_{n+1}=1$.

Title | autonomous system |

Canonical name | AutonomousSystem |

Date of creation | 2013-03-22 13:37:26 |

Last modified on | 2013-03-22 13:37:26 |

Owner | Daume (40) |

Last modified by | Daume (40) |

Numerical id | 6 |

Author | Daume (40) |

Entry type | Definition |

Classification | msc 34A99 |

Synonym | autonomous |

Synonym | autonomous equation |

Synonym | nonautonomous |

Synonym | nonautonomous equation |

Related topic | TimeInvariant |

Related topic | SystemDefinitions |

Defines | nonautonomous system |