Center or Limit Cycle: Renormalization Group as a Probe

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.

References in corpus (3)

• Limit cycles in quantum theories
• The Repressor-Lattice: Feed-Back, Commensurability, and Dynamical Frustration
• Renormalization Reductions for Systems with Delay

Cited by in corpus (9)

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• Reduction of Kinetic Equations to Liénard-Levinson-Smith Form: Counting Limit Cycles
• Where the Liénard--Levinson--Smith (LLS) theorem cannot be applied for a generalised Liénard system
• Suppressing birhythmicity by parametrically modulating nonlinearity in limit cycle oscillators
• When an oscillating center in an open system undergoes power law decay
• Renormalization group and isochronous oscillations
• A Study of the forced Van der Pol generalized oscillator with renormalization group method