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