SINGULARITY STRUCTURE OF 3RD-ORDER DYNAMICAL-SYSTEMS .2.

The singularity structure of the solutions of a general third-order sy stem, with polynomial right-hand sides of degree less than or equal to two, is studied about a movable singular point, An algorithm for tran sforming the given third-order system to a third-order Briot-Bouquet s ystem is presented, The dominant behavior of a solution of the given s ystem 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 ne ighborhood of the singularity is ensured, This algorithm is used to st udy the singularity structure of the solutions of the Lorenz system, t he Rikitake system, the three-wave interaction problem, the Rabinovich system, the Lotka-Volterra system, and the May-Leonard system for dif ferent sets of parameter values. The proposed approach goes far beyond the ARS algorithm.