Slow passage through a steady bifurcation: delay and memory effects
The authors consider the following problem as a model for the slow passage through a steady bifurcation: dy/dt = lambda(t) y - y/sup 3/ + delta, where lambda is a slowly increasing function of t given by lambda = lambda/sub i/ + epsilon t (lambda/sub i/ < 0). Both epsilon and delta are small parameters. This problem is motivated by laser experiments as well as theoretical studies of laser problems. In addition, this equation is a typical amplitude equation for imperfect steady bifurcations with cubic nonlinearities. When delta = 0, they have found that lambda = 0 is not the point where the bifurcation transition is observed. This transition appears at a value lambda = lambda/sub j/ > 0. They call lambda/sub j/ the delay of the bifurcation transition. They study this delay as a function of lambda/sub i/, the initial position of lambda, and delta, the imperfection parameter. To this end, they propose an asymptotic study of this equation as delta ..-->.. 0, epsilon small but fixed. Their main objective is to describe this delay in terms of the relative magnitude of delta and epsilon. Since time-dependent imperfections are always present in experiments, they analyze in the second part of the paper the effect of a small-amplitude but time-periodic imperfection given by delta(t) = delta cos(sigma t).
- Research Organization:
- Universite Libre de Bruxelles (Belgium)
- OSTI ID:
- 5322992
- Journal Information:
- J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 48:5/6; ISSN JSTPB
- Country of Publication:
- United States
- Language:
- English
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BEAM SPLITTING
BOUNDARY CONDITIONS
ELECTROMAGNETIC RADIATION
INSTABILITY
LASER RADIATION
LASERS
LIGHT TRANSMISSION
MECHANICS
NONLINEAR OPTICS
OPTICS
PERTURBATION THEORY
QUANTUM ELECTRONICS
RADIATIONS
STATISTICAL MECHANICS
TIME DEPENDENCE