Singularity structure of third-order dynamical systems. I

Sachdev, P. L. ; Ramanan, Sharadha (1997) Singularity structure of third-order dynamical systems. I Studies in Applied Mathematics, 98 (3). pp. 255-275. ISSN 0022-2526

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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.

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Deposited On:30 Mar 2011 13:36
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