Center or limit cycle: renormalization group as a probe
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...
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| Published in: | The European physical journal. D, Atomic, molecular, and optical physics Vol. 64; no. 2-3; pp. 479 - 489 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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01-10-2011
EDP Sciences |
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| 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. |
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| AbstractList | 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. |
| Author | Chakraborty, S. Bhattacharjee, J. K. Banerjee, D. B. Sarkar, A. |
| Author_xml | – sequence: 1 givenname: A. surname: Sarkar fullname: Sarkar, A. email: amarta345@bose.res.in organization: Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences – sequence: 2 givenname: J. K. surname: Bhattacharjee fullname: Bhattacharjee, J. K. organization: Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences – sequence: 3 givenname: S. surname: Chakraborty fullname: Chakraborty, S. organization: NBIA, Niels Bohr Institute – sequence: 4 givenname: D. B. surname: Banerjee fullname: Banerjee, D. B. organization: Department of Physics, Jadavpur University |
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| Cites_doi | 10.1103/PhysRevLett.90.174301 10.1103/PhysRevLett.103.118101 10.1103/PhysRevLett.94.158104 10.1016/S0020-7462(98)00048-1 10.1103/PhysRevLett.73.1311 10.1063/1.4823332 10.1103/PhysRevLett.64.1361 10.1073/pnas.89.9.3977 10.1103/RevModPhys.66.1481 10.1103/PhysRevE.54.376 10.1209/0295-5075/91/60004 10.1063/1.528326 10.1103/PhysRevLett.89.230401 10.1093/oso/9780198565635.001.0001 10.1103/PhysRevE.49.157 10.1103/PhysRevLett.101.086102 10.1103/PhysRevLett.90.238102 10.1103/PhysRevLett.93.069401 10.1143/PTP.118.211 10.1103/PhysRevLett.96.244101 10.1103/PhysRevLett.70.3361 10.1088/1751-8113/43/6/062001 10.1021/ja00181a011 10.1073/pnas.86.1.142 10.1111/j.1432-1033.1968.tb00175.x 10.1103/PhysRevE.52.222 10.1016/S0020-7462(98)00085-7 10.1038/nature01259 10.1103/PhysRevLett.72.76 |
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| Keywords | 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 |
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| Title | Center or limit cycle: renormalization group as a probe |
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