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On a class of nonlinear stochastic dynamical systems: Analysis of the transient behaviour. (English) Zbl 0626.60061
This paper considers a class of nonlinear dynamical systems with random parameters and inputs to determine the transient time evolution of the mean value of the dependent variable. Both the stochastic averaging method, developed by the author [Proc. IMACS Conf., Oslo 1985, Vol. 4, 257-260 (1985)] as an extension to the Bogolyubov method, and the decomposition method of the reviewer [Stochastic systems. (1983; Zbl 0523.60056)] are used with an application to a stochastic Van der Pol equation. A comparison of solutions and range of applicability is provided.
Reviewer: G.Adomian

60H99 Stochastic analysis
Full Text: DOI
[1] Bellomo, N; Cafaro, E; Rizzi, G, On the mathematical modelling of physical systems by ordinary differential stochastic equations, Math. comput. simulation, 361-367, (1984), (26) · Zbl 0547.60060
[2] Bonzani, I, Analysis of stochastic van der Pol oscillators using the decomposition method, (), 257-260
[3] Nayfeh, A.H, Perturbation methods, (1973), Wiley New York · Zbl 0375.35005
[4] Adomian, G, Stochastic systems, (1983), Academic Press New York · Zbl 0504.60066
[5] Gabetta, E, On a class of semilinear stochastic systems in mechanics with quadratic type nonlinearities, J. math. anal. appl., 118, 1-14, (1986) · Zbl 0614.60054
[6] Tsokos, C.P; Padgett, W.J, Random integral equations with applications to stochastic systems, (1971), Springer-Verlag New York · Zbl 0221.60072
[7] Riganti, R, On a class of nonlinear systems: the structure of a differential operator in the application of the decomposition method, J. math. anal. appl., 124, 189-199, (1987) · Zbl 0624.34036
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