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.
