应用数学2026，Vol.39Issue(3)：897-905,9.
二维环面上不可压缩磁流体力学五模类洛伦兹系统的动力学行为与数值模拟
The Dynamical Behavior and the Numerical Simulation of a Five-Mode Lorenz-like System of the MHD Equations for a Two-Dimensional Incompressible Fluid on a Torus
摘要
Abstract
A model obtained by a five-mode truncation of the magnetic hydrodynamic(MHD)equations for a two-dimensional incompressible fluid on a torus T2=[0,2π]×[0,2π]is studied.We derive a five-mode truncated system via Fourier expansion and analyze the stability of its equilibria.Subsequently,Hopf bifurcation and chaotic dynamics are identified,with the existence of a global attractor proven.Finally,detailed numerical simulations illustrate the transition from bifurcation to chaos.关键词
霍普夫分岔/李雅普诺夫函数/奇异吸引子Key words
Hopf bifurcation/Lyapunov function/Chaotic attractor分类
数理科学引用本文复制引用
王贺元,何香红..二维环面上不可压缩磁流体力学五模类洛伦兹系统的动力学行为与数值模拟[J].应用数学,2026,39(3):897-905,9.基金项目
Supported by NSFC(11572146),the Research Projects Foundation of GuangDong University of Science and Technology(GKY-2025KYZDK-25),the PhD Research Startup Foundation of GuangDong University of Science and Technology(GKY-2022BSQD-36) （11572146）
