Sachdev, PL and Ramanan, Sharadha
(1997)
*Singularity structure of third-order dynamical systems .2.*
In: Studies in Applied Mathematics, 98
(3).
pp. 277-310.

## Abstract

The singularity structure of the solutions of a general third-order system, with polynomial right-hand sides of degree less than or equal to two, is studied about a movable singular point, An algorithm for transforming the given third-order system to a third-order Briot-Bouquet system is presented, The dominant behavior of a solution of the given system near a movable singularity is used to construct a transformation that changes the given system directly to a third-order Briot-Bouquet system. The results of Horn for the third-order Briot-Bouquet system are exploited to give the complete form of the series solutions of the given third-order system; convergence of these series in a deleted neighborhood of the singularity is ensured, This algorithm is used to study the singularity structure of the solutions of the Lorenz system, the Rikitake system, the three-wave interaction problem, the Rabinovich system, the Lotka-Volterra system, and the May-Leonard system for different sets of parameter values. The proposed approach goes far beyond the ARS algorithm.

Item Type: | Journal Article |
---|---|

Publication: | Studies in Applied Mathematics |

Publisher: | John Wiley and Sons |

Additional Information: | Copyright of this article belongs to John Wiley and Sons. |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 30 Jun 2011 12:09 |

Last Modified: | 16 Oct 2018 07:24 |

URI: | http://eprints.iisc.ac.in/id/eprint/38454 |

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