## Abstract

The normal form theory of Poincaré, Siegel and Arnol'd is applied to an analytically solvable Lotka-Volterra system in the plane, and a periodically forced, dissipative Duffing's equation with chaotic orbits in its 3-dimensional phase space. For the planar model, we determine exactly how the convergence region of normal forms about a nodal fixed point is limited by the presence of singularities of the solutions in the complex t-plane. Despite such limitations, however, we show, in the case of a periodically driven system, that normal forms can be used to obtain useful estimates of the basin of attraction of a stable fixed point of the Poincaré map, whose "boundary" is formed by the intersecting invariant manifolds of a second hyperbolic fixed point nearby.

Original language | English |
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Pages (from-to) | 34-50 |

Number of pages | 17 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 33 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Jan 1 1988 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics