Non-Lorentzian spectral lineshapes near a Hopf bifurcation

被引：12
作者：
Gleeson, J. P. [1 ]
O'Doherty, F. [1 ]
机构：
[1] Natl Univ Ireland Univ Coll Cork, Cork, Ireland
来源：
SIAM JOURNAL ON APPLIED MATHEMATICS | 2006年 / 66卷 / 05期
关键词：
white noise; stochastic differential equations; Hopf normal form; Fokker-Planck equation; semiconductor lasers; oscillators;
D O I：
10.1137/040615146
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The effects of additive white noise upon the dynamics of a system described by its normal form are investigated, with particular reference to the well-known model of a detuned mode laser. The power spectrum corresponding to the laser amplitude is determined finite-difference solution of a partial differential equation, and analytical formulas are determined in asymptotic limits of large parameters. The effect of the amplitude-phase coupling parameter generating non-Lorentzian lineshapes is highlighted, and the regions of parameter space where first-eigenvalue approximations of the Fokker-Planck equation exist are indicated.
引用
收藏
页码：1669 / 1688
页数：20
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