Center or limit cycle: renormalization group as a probe

TY - JOUR

T1 - Center or limit cycle

T2 - renormalization group as a probe

AU - Sarkar, A.

AU - Bhattacharjee, J.K.

AU - Chakraborty, Sagar

AU - Banerjee, D.B.

PY - 2011/10/1

Y1 - 2011/10/1

N2 - 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.

AB - 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.

U2 - 10.1140/epjd/e2011-20060-1

DO - 10.1140/epjd/e2011-20060-1

M3 - Journal article

SN - 1434-6060

VL - 64

SP - 479

EP - 489

JO - European Physical Journal D

JF - European Physical Journal D

IS - 2-3

ER -