Consider the general system of two first-order Ordinary Differential Equations

(1) | |||

(2) |

Let and denote Fixed Points with , so

(3) | |||

(4) |

Then expand about so

(5) | |||

(6) |

To first-order, this gives

(7) |

In general, given an -D Map
, let be a Fixed Point, so that

(8) |

(9) |

so

(10) |

(11) |

(12) |

(13) |

(14) |

**References**

Tabor, M. ``Linear Stability Analysis.'' §1.4 in
*Chaos and Integrability in Nonlinear Dynamics: An Introduction.* New York: Wiley, pp. 20-31, 1989.

© 1996-9

1999-05-25