American Society of Civil Engineers

Bifurcations in Stochastic Systems—A Generalized Hermite Analysis

by Walter V. Wedig, (Univ of Karlsruhe, Germany)

pp. 1255-1262

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Document type: Conference Proceeding Paper
Part of: Structural Safety and Reliability
Abstract: Ito calculus and Markov theory are powerful tools to investigate nonlinear dynamic systems. Consequently, we need an extended experience to solve Fokker-Planck equations. In a more recent approach generalized Hermite polynomials are introduced to calculate eigenvalues and eigenvectors of parabolic operators. Applications are discussed for nonlinear dynamic systems with parameter fluctuations or external excitations.

ASCE Subject Headings:
Nonlinear systems
Spectral analysis

Author Keywords:
Mathematical Techniques--Polynomials - Statistical Methods - Vibrations--Spectrum Analysis
Bifurcations - Hermite Analysis - Lyapunov Exponents - Nonlinear Systems - Parabolic Operators - Stochastic Systems