Renormalization Group as a Probe for Dynamical Systems

• 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
• ISSN: 1742-6596; 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/319/1/012017

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.