Isaac Scientific Publishing

Journal of Advances in Applied Mathematics

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

Download PDF (989.1 KB) PP. 160 - 174 Pub. Date: July 12, 2016

DOI: 10.22606/jaam.2016.13003


  • Juan F. Navarro*
    Department of Applied Mathematics, University of Alicante, 03009 San Vicente del Raspeig, Alicante, Spain


The Poincaré–Lindstedt method in perturbation theory is used to compute periodic solutions in perturbed differential equations through a nearby periodic orbit of the unperturbed problem. The adaptation of this technique to systems of differential 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 differential equations of first order. The algorithm is based on an optimized adaptation of the Poincaré–Lindstedt technique to differential 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


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