...Edmon Perkins; Tim Fitzgerald For stochastic systems, the Fokker–Planck equation (FPE) is used to describe the system dynamics. The FPE is a partial differential equation, which is a function of all the variables in state space and of time. To solve the FPE, several methods are used, including...

... Stochastic systems Structural dynamics Uncertainty quantification A large class of physical systems in engineering and science can be modeled by stochastic differential equations. For many of these systems, the dominant source of uncertainty is due to the forcing which can be modeled...

..., 2018. Assoc. Editor: Xiaobo Yang. 06 09 2017 12 12 2017 Multibody system dynamics Design optimization Railroad dynamics Stochastic systems Design sensitivity Nonlinear systems As a multiple-degree-of-freedom (DOF) system, the dynamic vehicle–track interactions...

... Oscillators and Their Behaviour , Wiley , New York . [3] Jung , P. , 1993 , “ Periodically Driven Stochastic Systems ,” Phys. Rep. , 234 ( 4–5 ), pp. 175 – 295 . 10.1016/0370-1573(93)90022-6 [4] Ellermann , K. , 2005 , “ On the Determination of Nonlinear Response Distributions...

... manuscript received December 25, 2016; published online May 4, 2017. Assoc. Editor: Haiyan Hu. 26 06 2016 25 12 2016 Fractional calculus Nonlinear phenomena Stochastic systems In recent years, derivatives and integrals of noninteger order have been extended to nonlinear...

.... C. C. , 1978 , “ Moment Equation Methods for Nonlinear Stochastic Systems ,” J. Math. Anal. Appl. , 65 ( 2 ), pp. 306 – 320 . 10.1016/0022-247X(78)90182-8 [18] Ibrahim , R. A. , 1978 , “ Stationary Response of a Randomly Parametric Excited Nonlinear System ,” ASME J. Appl. Mech...

... . Manuscript received June 27, 2016; final manuscript received September 3, 2016; published online December 5, 2016. Assoc. Editor: Stefano Lenci. 27 06 2016 03 09 2016 Nonlinear dynamical systems Nonlinear oscillations Nonlinear phenomena Stochastic systems Vibration Real...

... September 1, 2016. Assoc. Editor: Corina Sandu. 06 11 2015 03 07 2016 Bifurcations Nonlinear dynamical systems Stochastic systems Coupling misalignment in power generator set is a malfunction, which can cause undesired vibrations and bothersome noises during operation...

... November 30, 2015; final manuscript received May 18, 2016; published online June 9, 2016. Assoc. Editor: Corina Sandu. 30 11 2015 18 05 2016 Chaotic dynamics Nonlinear dynamical systems Nonlinear phenomena Stochastic systems The effect of noise on the dynamical behaviors...

... method, dotted line; Monte Carlo simulation, solid line. ( a ) S y 1 y 1 ; ( b ) S y 5 y 5 . 09 01 2007 23 07 2007 26 11 2007 Fourier transforms Monte Carlo methods spectral analysis stochastic systems power spectrum density...