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The Poincare-Lindstedt method in perturbation theory is used to compute periodic solutions in perturbed dierential equations through a nearby periodic orbit of the unperturbed problem. The adaptation of this technique to systems of dierential equations of first order could produce meaningful advances in the qualitative analysis of many dynamical systems. In this paper, we present a new symbolic algorithm as well as a new symbolic computation tool to calculate periodic solutions in systems of dierential equations of first order. The algorithm is based on an optimized adaptation of the Poincare-Lindstedt technique to dierential systems. This algorithm is applied to compute a periodic solution in a Lotka-Volterra system.

A Symbolic Algorithm for the Computation of Periodic Orbits in Non–Linear Differential Systems