A Statistical Theory for Imperfect Bifurcation
Copyright policy )A Statistical Theory for Imperfect Bifurcation
An “honest” statistical method is presented to analyze the effects of imperfections and other disturbances on the bifurcation of solutions of nonlinear problems. First, uniformly valid asymptotic approximations of the solutions are obtained for any realization of the imperfections. The approximations are valid as the magnitude of the imperfections approaches zero. The statistical properties of the solutions are then deduced directly from these approximations, for specified statistics of the imperfections. For simplicity of presentation, the imperfections are taken as zero-mean, wide-sense stationary, Gaussian random processes. The statistical analysis is elementary. It provides easily analyzed results for the expected values and variances of the solutions. Confidence limits are also given. Application is given to a nonlinear boundary value problem.
Bifurcations in context of PDEs, random disturbances, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Equations involving nonlinear operators (general), amplitude of random perturbations, Gaussian random process, PDEs with randomness, stochastic partial differential equations, Stochastic stability in control theory
Bifurcations in context of PDEs, random disturbances, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Equations involving nonlinear operators (general), amplitude of random perturbations, Gaussian random process, PDEs with randomness, stochastic partial differential equations, Stochastic stability in control theory
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!