Lorenz系统长程相关性研究  

The research on long range correlation of Lorenz system

作　　者：王启光[1,2] 支蓉[3,4] 张增平[1,4] 

机构地区：[1]扬州大学物理科学与技术学院,扬州225002 [2]中国科学院大气物理研究所东亚区域气候-环境重点实验室,北京100029 [3]兰州大学大气科学学院,兰州730000 [4]国家气候中心,中国气象局气候研究开放实验室,北京100081

出　　处：《物理学报》2008年第8期5343-5350,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:40675044);国家重点基础研究发展规划(批准号:2006CB400503);国家科技支撑计划(批准号:2007BAC03A01)资助的课题~~

摘　　要：以典型的混沌系统——Lorenz系统为研究对象,运用去趋势涨落分析方法对不同初值和不同参数条件下系统的长程相关性进行研究.结果表明:系统长程相关性与系统初值所处相空间位置有关,初值越靠近不稳定平衡点,系统长程相关性越强,其标度指数α就越大,系统可预测性也就越好.当系统完全处于混沌状态时,随着控制参数r逐步增大其动力学结构的混沌特性更加明显,标度指数α都呈下降趋势,系统长程相关性逐渐减弱,系统可预测性也随之减弱.这揭示了长程相关性与系统可预测性的对应关系.对系统进行扰动后发现,当加入随机噪声后系统长程相关性随噪声强度增大而逐渐减弱.这进一步表明Lorenz系统长程相关性(标度指数α)是表征其可预测性的极其有效的物理量之一.This paper takes the typical chaotic system,the Lorenz system,as the subject.We use the detrended fluctuation analysis method to study the system＇s long-range correlation for different initial values and parameters.It turns out that the system＇s long range correlation is related with its initial value＇s phase space position.When the initial value is close to the unstable equilibrium points,the system＇s long rang correlation is strengthened,the scaling exponents α are bigger,and the predictability of the system is better.When the system is in complete chaotic state,its long range correlation becomes weak with the parameters increasing,and the scaling exponents α are decrease,the predictability of the system becomes weaker.This reveals the relationship between the system＇s long range correlation and its predictability.We disturbed the system equation with random noise and found that the system＇s long range correlation decreases with the increase of random noise intensity.This result further signifies out that the Lorenz system＇s long range correlation is a physical parameter that may serves as an effective predictability criterion.

关 键 词：LORENZ系统 长程相关性 去趋势涨落分析 可预测性 

分 类 号：O415.5[理学—理论物理] TP316.2[理学—物理]