On the application of the Lindstedt-Poincar\'{e} method to the Lotka-Volterra system

TL;DR

This paper applies the Lindstedt-Poincaré perturbation method to the Lotka-Volterra system, providing a systematic algorithm that yields many corrections and estimates the convergence radius of the series.

Contribution

It introduces an efficient algorithm for applying the Lindstedt-Poincaré method to multi-variable systems like Lotka-Volterra, enhancing perturbation analysis capabilities.

Findings

Generated a large number of perturbation corrections

Estimated the convergence radius of the series

Demonstrated applicability to systems with multiple variables

Abstract

We apply the Lindstedt-Poincar\'{e} method to the Lotka-Volterra model and discuss alternative implementations of the approach. By means of an efficient systematic algorithm we obtain an unprecedented number of perturbation corrections for the two dynamical variables and the frequency. They enable us to estimate the radius of convergence of the perturbation series for the frequency as a function of the only model parameter. The method is suitable for the treatment of systems with any number of dynamical variables.