The effect of random phase on the Josephson junction system dynamic model is investigated.It is shown that random phase has the suppressing ability for controlling chaos.The top Lyapunov exponent is used to detect the...The effect of random phase on the Josephson junction system dynamic model is investigated.It is shown that random phase has the suppressing ability for controlling chaos.The top Lyapunov exponent is used to detect the chaotic dynamics in the system,and the method for calculating the top Lyapunov exponent is based on Khasminskii’s spherical coordinate formulation for linear stochastic systems.In addition,Poincarémap,phase portraits and time evolution are investigated to verify the obtained results.It is found that these results have the excellent agreement.展开更多
The reliability of quasi integrable and non-resonant Hamiltonian system under fractional Gaussian noise(fGn)excitation is studied.Noting rather flat fGn power spectral density(PSD)in most part of frequency band,the fG...The reliability of quasi integrable and non-resonant Hamiltonian system under fractional Gaussian noise(fGn)excitation is studied.Noting rather flat fGn power spectral density(PSD)in most part of frequency band,the fGn is innovatively regarded as a wide-band process.Then,the stochastic averaging method for quasi integrable Hamiltonian systems under wide-band noise excitation is applied to reduce 2n-dimensional original system into n-dimensional averaged ltd stochastic differential equations(SDEs).Reliability function and mean first passage time are obtained by solving the associated backward Kolmogorov equation and Pontryagin equation.The validity of the proposed procedure is tested by applying it to an example and comparing the numerical results with those from Monte Carlo simulation.展开更多
文摘The effect of random phase on the Josephson junction system dynamic model is investigated.It is shown that random phase has the suppressing ability for controlling chaos.The top Lyapunov exponent is used to detect the chaotic dynamics in the system,and the method for calculating the top Lyapunov exponent is based on Khasminskii’s spherical coordinate formulation for linear stochastic systems.In addition,Poincarémap,phase portraits and time evolution are investigated to verify the obtained results.It is found that these results have the excellent agreement.
基金supported by National Key R&D Program of China(Grant No.2018 YFC0809400)Zhejiang Provincial Natural Science Foundation of China(Grant No.LY16A020001)National Natural Science Foundation of China(Grant No.11802267).
文摘The reliability of quasi integrable and non-resonant Hamiltonian system under fractional Gaussian noise(fGn)excitation is studied.Noting rather flat fGn power spectral density(PSD)in most part of frequency band,the fGn is innovatively regarded as a wide-band process.Then,the stochastic averaging method for quasi integrable Hamiltonian systems under wide-band noise excitation is applied to reduce 2n-dimensional original system into n-dimensional averaged ltd stochastic differential equations(SDEs).Reliability function and mean first passage time are obtained by solving the associated backward Kolmogorov equation and Pontryagin equation.The validity of the proposed procedure is tested by applying it to an example and comparing the numerical results with those from Monte Carlo simulation.
