Renormalization Group as a Probe for Dynamical Systems

The use of renormalization group (RG) in the analysis of nonlinear dynamical problems has been pioneered by Goldenfeld and co-workers [1]. We show that perturbative renormalization group theory of Chen et al can be used as an effective tool for asymptotic analysis for various nonlinear dynamical osc...

Full description

Saved in:
Bibliographic Details
Published in:Journal of physics. Conference series 2011-09, Vol.319 (1), p.012017-11
Main Authors: Sarkar, Amartya, Bhattacharjee, J K
Format: Article
Language:English
Subjects:
Asymptotic properties
Classification
Dynamical systems
Group theory
Methodology
Nonlinear dynamics
Nonlinear systems
Nonlinearity
Orbits
Oscillators
Physics
Stability analysis
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The use of renormalization group (RG) in the analysis of nonlinear dynamical problems has been pioneered by Goldenfeld and co-workers [1]. We show that perturbative renormalization group theory of Chen et al can be used as an effective tool for asymptotic analysis for various nonlinear dynamical oscillators. Based on our studies [2] done on two-dimensional autonomous systems, as well as forced non-autonomous systems, we propose a unified methodology – that uses renormalization group theory – for finding out existence of periodic solutions in a plethora of nonlinear dynamical systems appearing across disciplines. The technique will be shown to have a non-trivial ability of classifying the solutions into limit cycles and periodic orbits surrounding a center. Moreover, the methodology has a definite advantage over linear stability analysis in analyzing centers.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/319/1/012017