Computation of periodic orbits in three‐dimensional Lotka‐Volterra systems

摘要

>This paper deals with an adaptation of the Poincaré‐Lindstedt method for the determination of periodic orbits in three‐dimensional nonlinear differential systems. We describe here a general symbolic algorithm to implement the method and apply it to compute periodic solutions in a three‐dimensional Lotka‐Volterra system modeling a chain food interaction. The sufficient conditions to make secular terms disappear from the approximate series solution are given in the paper.