First-passage failure of harmonically and stochastically excited strongly nonlinear oscillators with

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  The time delay in control is an important research subject.Many researches on the deterministic systems with time delay have been made [1-5], while the study on that for stochastic systems is very limited.The controlled linear systems with deterministic and random time delays subjected to Gaussian white noise excitations have been studied by Grigoriu [6].The effects of the time delay on the control of nonlinear systems under Gaussian white noise excitations have been studied by Bilello et al [7].Recently.the response of quasi-integrable Hamiltonian systems with delayed feedback control under Gaussian white noise excitation has been studied by Zhu and Liu [8] using the stochastic averaging method.
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