A Study of the forced Van der Pol generalized oscillator with renormalization group method

TL;DR

This paper applies the renormalization group method to analyze the forced Van der Pol generalized oscillator, deriving its asymptotic solution and demonstrating the method's efficiency through numerical simulations.

Contribution

It introduces the application of the renormalization group technique to the forced Van der Pol generalized oscillator for the first time.

Findings

Successful derivation of asymptotic solutions

Effective use of renormalization group method

Numerical simulations confirm analytical results

Abstract

In this paper the equation of forced Van der Pol generalized oscillator is examined with renormalization group method. A brief recall of the renormalization group technique is done. We have applied this method to the equation of forced Van der Pol generalized oscillator to search for its asymptotic solution and its renormalization group equation. The analysis of the numerical simulation graph is done; the method's efficiency is pointed out.