磁流体动力学截断方程组的动力学行为研究

摘要

本文研究了平面正方形区域上不可压缩的磁流体动力学方程组的动力学行为问题.利用模式截断的方法,获得了一个全新的十模类Lorenz方程组,求得了此方程组的平衡点,分析了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,并对其动力学行为进行了数值模拟.%In this paper,the MHD equations for two-dimensional incompressible fluid on a torus is researched,a new ten-mode Lorenz equations is obtained by mode truncation.The equilibrium point is figured out and the stability is analyzed,the existence of the attractor is proved.The global stability of the equations is discussed,and the dynamical behavior is simulated numerically by computer.