Center or limit cycle: renormalization group as a probe

• Published in: The European physical journal. D, Atomic, molecular, and optical physics Vol. 64; no. 2-3; pp. 479 - 489
• Main Authors: Sarkar, A., Bhattacharjee, J. K., Chakraborty, S., Banerjee, D. B.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-10-2011; EDP Sciences
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Atomic; Classification; Dynamical systems; Exact sciences and technology; Group theory; Methodology; Molecular; Nonlinear dynamics; Nonlinear dynamics and nonlinear dynamical systems; Nonlinearity; Optical and Plasma Physics; Orbits; Physical Chemistry; Physics; Physics and Astronomy; Quantum Information Technology; Quantum Physics; Regular Article; Spectroscopy/Spectrometry; Spintronics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Two dimensional; Nonlinear Dynamical System; Periodic Solution; Renormalization Group; Linear Stability Analysis; Periodic Orbit; Renormalization group method; Group theory; Theoretical study; Periodic orbit; Nonlinear dynamical systems; Time delay; Periodic solution
• ISSN: 1434-6060; 1434-6079
• DOI: 10.1140/epjd/e2011-20060-1

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.