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Singularity Structure of Third-Order Dynamical Systems. I

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
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 28 Feb 2008
Last Modified: 19 Sep 2010 04:42
URI: http://eprints.iisc.ernet.in/id/eprint/13106

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