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

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.