Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 66, Issue 5, Pages 1669-1688Publisher
SIAM PUBLICATIONS
DOI: 10.1137/040615146
Keywords
white noise; stochastic differential equations; Hopf normal form; Fokker-Planck equation; semiconductor lasers; oscillators
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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.
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