The first-passage statistics of Duffing-Rayleigh- Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed int...The first-passage statistics of Duffing-Rayleigh- Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed into two time homogeneous diffusion Markovian processes of amplitude and phase after stochastic averaging. The diffusion process method for first-passage problem is used and the corresponding backward Kolmogorov equation and Pontryagin equation are constructed and solved to yield the conditional reliability function and mean first-passage time with suitable initial and boundary conditions. The analytical results are confirmed by Monte Carlo simulation.展开更多
This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment sta...This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment stability property of the viscoelastic system,we use the stochastic averaging method,Girsanov theorem and Feynmann-Kac formula to derive the approximate analytic expansion of the moment Lyapunov exponent.Furthermore,the Monte Carlo simulation results for the original system are given to check the accuracy of the approximate analytic results.At the end of this paper,results are presented to show some quantitative pictures of the effects of the system parameters,noise parameters and viscoelastic parameters on the stability of the viscoelastic plate.展开更多
基金the Foundation of ECUST(East China University of Science and Technology)for Outstanding Young Teachers(YH0157105)
文摘The first-passage statistics of Duffing-Rayleigh- Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed into two time homogeneous diffusion Markovian processes of amplitude and phase after stochastic averaging. The diffusion process method for first-passage problem is used and the corresponding backward Kolmogorov equation and Pontryagin equation are constructed and solved to yield the conditional reliability function and mean first-passage time with suitable initial and boundary conditions. The analytical results are confirmed by Monte Carlo simulation.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11072107 and 91016022)the Specialized Research Fund for the Doctoral Program of Higher Education of China (GrantNo.20093218110003)
文摘This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment stability property of the viscoelastic system,we use the stochastic averaging method,Girsanov theorem and Feynmann-Kac formula to derive the approximate analytic expansion of the moment Lyapunov exponent.Furthermore,the Monte Carlo simulation results for the original system are given to check the accuracy of the approximate analytic results.At the end of this paper,results are presented to show some quantitative pictures of the effects of the system parameters,noise parameters and viscoelastic parameters on the stability of the viscoelastic plate.
