Sachdev, PL and Ramanan, Sharadha (1997) Singularity structure of third-order dynamical systems .2. In: Studies in Applied Mathematics, 98 (3). pp. 277-310.Full text not available from this repository.
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|
|Additional Information:||Copyright of this article belongs to John Wiley and Sons.|
|Date Deposited:||30 Jun 2011 12:09|
|Last Modified:||30 Jun 2011 12:09|
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