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Invariant measures and Lyapunov exponents for generalized parameter fluctuations
AbstractFor the stability investigation of linear systems with parameter fluctuations we follow Khasminskii's concept to separate a stationary solution part by introducing polar coordinates. In the two-dimensional case this projection lives on the unit circle and determines the associated Lyapunov exponents according to Oseledec's multiplicative ergodic theorem.To avoid combersome phase process simulations and corresponding time-average evaluations we discuss simple integration routines of diffusion equations for calculating the invariant phase measures. Results are obtained for parametric excitation by white noise or by harmonic functions. Both cases are covered by a generalized fluctuation model, recently introduced.
Invariant measures and Lyapunov exponents for generalized parameter fluctuations
AbstractFor the stability investigation of linear systems with parameter fluctuations we follow Khasminskii's concept to separate a stationary solution part by introducing polar coordinates. In the two-dimensional case this projection lives on the unit circle and determines the associated Lyapunov exponents according to Oseledec's multiplicative ergodic theorem.To avoid combersome phase process simulations and corresponding time-average evaluations we discuss simple integration routines of diffusion equations for calculating the invariant phase measures. Results are obtained for parametric excitation by white noise or by harmonic functions. Both cases are covered by a generalized fluctuation model, recently introduced.
Invariant measures and Lyapunov exponents for generalized parameter fluctuations
Wedig, Walter V. (author)
Structural Safety ; 8 ; 13-25
1990-01-01
13 pages
Article (Journal)
Electronic Resource
English
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