五模类Lorenz方程组吸引子的存在性及计算机模拟  

Existence of the attractor and the numerical simulation of a five-modes Lorenz equation

作　　者：汪敬贤[1] 王贺元[2] 

机构地区：[1]渤海大学公共计算机教研部,锦州121001 [2]辽宁工业大学数理系,锦州121001

出　　处：《哈尔滨工业大学学报》2008年第4期670-672,共3页Journal of Harbin Institute of Technology

基　　金：辽宁省教育厅科研基金资助项目

摘　　要：为讨论类Lorenz方程组的动力学行为及数值模拟问题,采用新的截断模式对平面正方形区域上不可压缩的Navier-Stokes方程进行傅立叶展开后截断得到新五模类Lorenz方程组.分析和讨论方程组的全局稳定性,结果证明:方程组吸引子的存在性,得出了方程组的混沌行为的数值模拟结果.To discuss the dynamical behaviors and the numerical simulation of a Lorenz- like equation, we expanded the plane incompressible Navier- Stokes equations in fourier series on a torus, then the new five - modes Lorenz equations were obtained. The global stability of the equations was discussed, and the existence of the attractor was proved,the chaos behavior was simulated numerically by a computer.

关 键 词：NAVIER-STOKES方程 奇怪吸引子 李雅普诺夫函数 

分 类 号：O175.14[理学—数学] O241.81[理学—基础数学]