Scaling relations for forced oscillators in the transition from a dissipative to a Hamiltonian system

Karsten Flensberg; Henrik Svensmark

doi:10.1103/PhysRevE.47.2190

Scaling relations for forced oscillators in the transition from a dissipative to a Hamiltonian system

Karsten Flensberg, Henrik Svensmark

Faststoffysik

4 Citationer (Scopus)

Abstract

The dynamics and the stability of a forced damped nonlinear oscillator driven at twice its resonance frequency is studied. At the transition from a dissipative system to a Hamiltonian system, simple scalings relations are found by the use of the Floquet theory of the linearized problem. The Floquet exponents and the period-doubling bifurcation point are determined analytically in the limit of small damping. The theory is compared to numerical calculations on a Duffing oscillator and excellent agreement is found.

Originalsprog	Engelsk
Tidsskrift	Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Vol/bind	47
Udgave nummer	3
Sider (fra-til)	2190-2192
Antal sider	3
ISSN	1539-3755
DOI	https://doi.org/10.1103/PhysRevE.47.2190
Status	Udgivet - 1 mar. 1993

Adgang til dokumentet

10.1103/PhysRevE.47.2190

Citationsformater

@article{f7fa5a8d61f749f6ae5fe8a0e929fbd0,

title = "Scaling relations for forced oscillators in the transition from a dissipative to a Hamiltonian system",

abstract = "The dynamics and the stability of a forced damped nonlinear oscillator driven at twice its resonance frequency is studied. At the transition from a dissipative system to a Hamiltonian system, simple scalings relations are found by the use of the Floquet theory of the linearized problem. The Floquet exponents and the period-doubling bifurcation point are determined analytically in the limit of small damping. The theory is compared to numerical calculations on a Duffing oscillator and excellent agreement is found.",

author = "Karsten Flensberg and Henrik Svensmark",

year = "1993",

month = mar,

day = "1",

doi = "10.1103/PhysRevE.47.2190",

language = "English",

volume = "47",

pages = "2190--2192",

journal = "Physical Review E",

issn = "2470-0045",

publisher = "American Physical Society",

number = "3",

}

TY - JOUR

T1 - Scaling relations for forced oscillators in the transition from a dissipative to a Hamiltonian system

AU - Flensberg, Karsten

AU - Svensmark, Henrik

PY - 1993/3/1

Y1 - 1993/3/1

N2 - The dynamics and the stability of a forced damped nonlinear oscillator driven at twice its resonance frequency is studied. At the transition from a dissipative system to a Hamiltonian system, simple scalings relations are found by the use of the Floquet theory of the linearized problem. The Floquet exponents and the period-doubling bifurcation point are determined analytically in the limit of small damping. The theory is compared to numerical calculations on a Duffing oscillator and excellent agreement is found.

AB - The dynamics and the stability of a forced damped nonlinear oscillator driven at twice its resonance frequency is studied. At the transition from a dissipative system to a Hamiltonian system, simple scalings relations are found by the use of the Floquet theory of the linearized problem. The Floquet exponents and the period-doubling bifurcation point are determined analytically in the limit of small damping. The theory is compared to numerical calculations on a Duffing oscillator and excellent agreement is found.

U2 - 10.1103/PhysRevE.47.2190

DO - 10.1103/PhysRevE.47.2190

M3 - Journal article

C2 - 9960242

SN - 2470-0045

VL - 47

SP - 2190

EP - 2192

JO - Physical Review E

JF - Physical Review E

IS - 3

ER -