Sachdev, PL and Ramanan, Sharadha
(1997)
*Singularity Structure of Third-Order Dynamical Systems. I.*
In: Studies in Applied Mathematics, 98
(3).
pp. 255-275.

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## Abstract

A general third-order dynamical system with polynomial right-hand sides of finite degrees in the dependent variables is analyzed to unravel the singularity structure of its solutions about a movable singular point. To that end, the system is first transformed to a second-order Briot–Bouquet system and a third auxiliary equation via a transformation, similar to one used earlier by R. A. Smith in 1973–1974 for a general second-order dynamical system. This transformation imposes some constraints on the coefficients appearing in the general third-order system. The known results for the second-order Briot–Bouquet system are used to explicitly write out Laurent or psi-series solutions of the general third-order system about a movable singularity. The convergence of the relevant series solutions in a deleted neighborhood of the singularity is ensured. The theory developed here is illustrated with the help of the May–Leonard system.

Item Type: | Journal Article |
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Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Depositing User: | RM Shivakumara |

Date Deposited: | 28 Feb 2008 |

Last Modified: | 19 Sep 2010 04:42 |

URI: | http://eprints.iisc.ac.in/id/eprint/13106 |

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