Singularity structure of third-order dynamical systems. II

Sachdev, P. L. ; Ramanan, Sharadha (1997) Singularity structure of third-order dynamical systems. II Studies in Applied Mathematics, 98 (3). pp. 277-310. ISSN 0022-2526

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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:Article
Source:Copyright of this article belongs to John Wiley and Sons.
ID Code:33867
Deposited On:30 Mar 2011 13:36
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