九模类Lorenz系统的动力学行为及其数值模拟

The Dynamical Behavior and the Numerical Simulation of a Nine-Mode Lorenze Equations

本文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,利用模式截断方法得到了一个全新的九模类Lorenz方程组,求出该方程组的平衡点,分析其稳定性等动力学行为,证明了该类Lorenz方程组混沌吸引子的存在性,对其进行全局稳定性分析,并对其动力学行为进行数值模拟.

This paper deals with a research on the Navier-Stokes equations for two-dimen -sional incompressible fluid on a torus. The new nine-mode Lorenz equations have been obtained by mode truncation. The equilibrium point has been figured out and the stability has been analyzed. The existence of the attractor has been proved, the global stability of the equations has bcen disscused and the dynamical behavior has been simulated numerically by computer.