Titlebook: Nonlinear Stochastic Dynamic Engineering Systems; IUTAM Symposium Inns F. Ziegler,G. I. Schu?ller Conference proceedings 1988 Springer-Verl

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Chaos in Nonlinear Systems Subjected to Small Random Perturbationsministic systems modeled by a one-dimensional mapping are analyzed when the system is perturbed by a multiplicative and an additive noise. Stochastic versions of invariant measure and Lyapunov exponent are calculated and are comparatively discussed with deterministic ones, from the viewpoint of cons

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Stochastic Stability of Modes at Rest in Coupled Nonlinear Systemse subjected to external random excitation. Sufficient conditions for stability of the rest modes are established and applied to examine the stability of pitching vibration in a nonlinear absorber subjected to a random vertical support excitation.

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Lyapunov Exponents of Nonlinear Stochastic Systemsts. The theory of Lyapunov exponents enables one to talk about stochastic stability, stochastic chaos and stochastic bifurcation of nonlinear stochastic systems in a way that is surprisingly analogous to the deterministic one.

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expdient

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Stability of Linear Differential Systems with Parametric ExcitationThe aim of this paper is to summarize both theoritical and numerical results concerning the dependence of the Lyapunov exponent of the solution of the solution of a linear equation, in terms of some parameters describing the law of the parametric excitation.