Symbolic computation of Lyapunov coefficients in a planar Bautin bifurcation

TL;DR

This paper presents a method for computing Lyapunov coefficients in planar Bautin bifurcations using complex variable transformations, with examples demonstrating the algorithm's effectiveness.

Contribution

It introduces a novel approach for calculating Lyapunov coefficients via complex normal form transformations in planar Bautin bifurcations.

Findings

Algorithms are consistent with theoretical expectations

Method successfully computes Lyapunov coefficients in examples

Provides a practical tool for bifurcation analysis

Abstract

Often in the study the periodic orbits in dynamical systems, the computation of the Lyapunov Coeficients is needed. In this paper, the calculations of this coeficients were done via complex variable transformation in order to obtain the complex normal form for a planar Bautin bifurcation. Some examples are given in order to verify the consistency of the algorithms.