lntegrability and singularity structure of predator-prey system

The extended ARS (Ablowitz, Ramani, and Segur) algorithm is introduced to characterize a dynamical system as Painlevi or otherwise; to that end, it is required that the formal series-the Laurent series, logarithmic, algebraic psi series about a movable singularity-are shown to converge in the deleted neigh-borhood of the singularity. The determinations thus obtained are compared with those following from the $\alpha$ method of Painlev’e. An attempt is made to relate the structure of solutions about a movable singularity with that of first integrals (when they exist), All these ideas are illustrated by a comprehensive analysis of the general two-dimensional predator-prey syste