We study a class of stochastic semilinear damped wave equations driven by additive Wiener noise.Owing to the damping term,under appropriate conditions on the nonlinearity,the solution admits a unique invariant distrib...We study a class of stochastic semilinear damped wave equations driven by additive Wiener noise.Owing to the damping term,under appropriate conditions on the nonlinearity,the solution admits a unique invariant distribution.We apply semi-discrete and fully-discrete methods in order to approximate this invariant distribution,using a spectral Galerkin method and an exponential Euler integrator for spatial and temporal discretization respectively.We prove that the considered numerical schemes also admit unique invariant distributions,and we prove error estimates between the approximate and exact invariant distributions,with identification of the orders of convergence.To the best of our knowledge this is the first result in the literature concerning numerical approximation of invariant distributions for stochastic damped wave equations.展开更多
This letter presents a new one-dimensional chaotic map with infinite collapses. Theoretical analyses show that the map has complicated dynamical behavior and ideal distribution.The map can be applied in chaotic spread...This letter presents a new one-dimensional chaotic map with infinite collapses. Theoretical analyses show that the map has complicated dynamical behavior and ideal distribution.The map can be applied in chaotic spreading spectrum communication and chaotic cipher.展开更多
In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales.We show by a combination of analytical arguments and numerical examp...In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales.We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale.This is due to the fact that such implicit methods cannot correctly capture non-Dirac invariant distributions when the time step size is much larger than the relaxation time of the system.展开更多
基金supported by the projects ADA(Grant No.ANR-19-CE40-0019-02)and SIMALIN(Grant No.ANR-19-CE40-0016)operated by the French National Research Agencysupported by the NSF of China(Grant Nos.11971488,12371417)supported by the China Scholarship Council(Grant No.202206370085)。
文摘We study a class of stochastic semilinear damped wave equations driven by additive Wiener noise.Owing to the damping term,under appropriate conditions on the nonlinearity,the solution admits a unique invariant distribution.We apply semi-discrete and fully-discrete methods in order to approximate this invariant distribution,using a spectral Galerkin method and an exponential Euler integrator for spatial and temporal discretization respectively.We prove that the considered numerical schemes also admit unique invariant distributions,and we prove error estimates between the approximate and exact invariant distributions,with identification of the orders of convergence.To the best of our knowledge this is the first result in the literature concerning numerical approximation of invariant distributions for stochastic damped wave equations.
基金National Natural Science Fundation of China(Grant No. 69735101)
文摘This letter presents a new one-dimensional chaotic map with infinite collapses. Theoretical analyses show that the map has complicated dynamical behavior and ideal distribution.The map can be applied in chaotic spreading spectrum communication and chaotic cipher.
基金ONR grant N00014-01-0674.TLi is partially supported by National Science Foundation of China grants 10401004the National Basic Research Program under grant 2005CB321704.
文摘In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales.We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale.This is due to the fact that such implicit methods cannot correctly capture non-Dirac invariant distributions when the time step size is much larger than the relaxation time of the system.
