EFFECTIVE DYNAMICS OF A COUPLED MICROSCOPIC-MACROSCOPIC STOCHASTIC SYSTEM

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence.     

关于一个扰动非线性薛定谔方程的注记

本文讨论了一个扰动非线性薛定谔方程对于Ｓｔｏｋｅｓ波的一类同宿轨道，证明了这类轨道是不存在的。     

ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN LEVY NOISES

Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies. A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian α-stable Lévy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation, or P-bifurcation, for stochastic differential equations with non-Gaussian Lévy noises.     

随机偏微分方程——建模,分析与有效动力学

综述随机偏微分方程的基本概念、理论、方法与应用,内容包括Hilbert空间中的Wiener过程、Ito随机积分、随机偏微分方程的解及其有效动力学。还介绍了随机偏微分方程的粗糙轨道、正则结构以及在Kardar-ParisiZhang(KPZ)方程中的应用。还介绍了段金桥与王伟的著作《Effective Dynamics of Stochastic Partial Differential Equations(随机偏微分方程的有效动力学)》的基本内容。     

Averaging principle for quasi-geostrophic motion under rapidly oscillating forcing

1　IntroductionandtheProblemPresentedClimateandgeophysicalflowsdefinetheenvironmentinwhichwelive ,andtheirunderstanding,beyondbeingafascinatingscientificchallenge,isoftremendouseconomicandsocialimportance.Aclassoflargescalegeophysicalfluidflows,suchastheGulfStreamandoceanicgyres,aremodelledbythequasi_geostrophicequation .Thequasi_geostrophic (QG)equationmodelsaclassoflargescalegeophysicalflows.ItisderivedasanapproximationoftherotatingNavier_StokesequationsbyanasymptoticexpansioninasmallRos…     

A delay-dependent stability criterion for nonlinear stochastic delay-integro-differential equations

A type of complex systems under both random influence and memory effects is considered. The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations. A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough. Numerical simulations are presented to illustrate the theoretical result.     

具有快速振荡外力的拟地转运动的平均原理

一类大尺度的地球物理流体流可以用拟地转方程来描述．有限、但是大时间区间和整个时间轴上在快速振荡外力下的拟地转运动的平均原理被得到了．其中包括比较估计,稳定性估计和拟地转运动及其平均运动之间的收敛性．进一步,几乎周期拟地转运动的存在性和吸引子的收敛性也被得到了．     

什么是随机动力系统

微生物组学大数据在生态环境、人类健康和疾病研究方面都起到了重要作用。通过数学、统计等数据挖掘方法,从高维复杂数据中提取有用信息,是微生物组学大数据建模和分析的关键问题。本文分析了微生物组学大数据的特点,对当前数据分析和计算研究中存在的热点和难点进行了探讨分析,并综述了当前微生物组学大数据模式挖掘、网络重建与分析的研究概况。