Stochastic Bifurcation of Nonlinear Parametric Systems

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

Document Type: Proceeding Paper

Part of: Probabilistic Methods in Civil Engineering


Parametrically excited systems with progressive restorings possess two different solutions: the trivial one and a stationary branching process. The second solution is physically existent if the Lyapunov exponent of the linear solution is positive. To calculate both, Lyapunov exponents and stationary branching square means, the paper applies the multiplicative expectation theorem and orthogonal moment expansions.

Subject Headings: Stochastic processes | Parameters (statistics) | Nonlinear response | Stationary processes | Nonlinear analysis | Moment (mechanics) | Equations of motion

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