Eur. Phys. J. D 64, 479-489 (2011)
https://doi.org/10.1140/epjd/e2011-20060-1

Regular Article

Center or limit cycle: renormalization group as a probe

¹ Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, 700098 Kolkata, India
² NBIA, Niels Bohr Institute, Blegdamsvej 17, Copenhagen Ø 2100, Denmark
³ Department of Physics, Jadavpur University, 700032 Kolkata, India

^a e-mail: amarta345@bose.res.in

Received: 24 January 2011
Received in final form: 23 May 2011
Published online: 17 August 2011

Abstract

Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed 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.