Etude de l'oscillateur de Van der Pol g\'en\'eralis\'e par la m\'ethode du groupe de renormalisation

TL;DR

This paper applies the renormalization group method to analyze the asymptotic behavior of a generalized Van der Pol oscillator, a model relevant to various physical phenomena, providing insights into its long-term dynamics.

Contribution

It demonstrates the application of the renormalization group technique to a generalized Van der Pol oscillator, extending previous methods to more complex models.

Findings

Asymptotic solutions derived for the generalized Van der Pol oscillator

The renormalization group method effectively captures long-term behavior

Enhanced understanding of physical phenomena modeled by the oscillator

Abstract

The renormalization group method is one of the singular perturbation methods used in the research of the asymptotic behavior of solution of ordinary differential equations. In this paper, the equation of VAN der Pol generalized oscillator that models many physical phenomena is considered. A brief review of the technique is done and is applied to the generalized VAN der Pol oscillator to highlight its asymptotic solution.