新五模类Lorenz系统的动力学行为分析及仿真  

Dynamicalbehavior analysis and numerical simulation of new five-mode Lorenz-like equations

作　　者：王贺元 李佳 王美玉 宋斯琦 王晓帆 曹婷婷 WANG Heyuan;LI Jia;WANG Meiyu;SONG Siqi;WANG Xiaofan;CAO Tingting(College of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2020年第2期164-170,共7页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金面上项目(11572146)。

摘　　要：流动的稳定性是应用数学和计算数学领域的重大课题。稳定性发生变化,流动的形态发生突变,与此有关的数学理论可用来解释湍流的生成机理。描述流体流动的Navier-Stokes方程无论在理论上和计算上都是物理和工程科学中的重大难题。此无穷维动力系统解的理论分析和数值仿真等问题都是极具挑战性的,因此必须进行有限维约化处理。基于惯性流形理论,采用简化模态的有限模态分析方法对Navier-Stokes方程解的性态进行定性分析和数值仿真。对区域[0,2π]×[0,2π]上不可压缩Navier-Stokes方程进行傅氏展开,约化得到五模的类Lorenz系统,讨论了系统吸引子的存在性,分析和讨论了系统的稳定性,对系统的动力学行为进行了数值仿真。揭示了系统动力学行为的演化过程。The stability of flows is a major topic in the field of applied mathematics and computational mathematics.Changes of stability can lead to sudden changes in the flow pattern.The related mathematical theory can be used to explain the mechanism of turbulence.The Navier-Stokes equations,which describe the flow of fluid in theory and computation,are important problems in physical and engineering science.The theoretical analysis and numerical simulation of the solution of the infinite dimensional dynamical system are very challenging,so it is necessary to deal with the finite dimensional reduction.Based on the inertial manifold theory,the finite mode analysis method of simplified modes is used to analyze the behavior of the solution of the Navier-Stokes equation qualitatively and numerically.The plane incompressible Navier-Stokes equations is expanded in Fourier series on a torus,and a five-mode Lorenz-like equations is obtained.The existence of the attractor is proved,and the stability of the equations is disscused.These reveal the evolution of system dynamics behavior.

关 键 词：Navier-Stokes方程 奇怪吸引子 李雅普诺夫指数 类LORENZ系统 

分 类 号：O175.1[理学—数学] O192[理学—基础数学]