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OA
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
本文研究通过对二维环面上不可压缩磁流体力学(MHD)方程进行五模截断得到的模型.首先,通过在傅里叶展开中选取五个模式推导得到模型系统,并讨论了该五模系统平衡点的稳定性;其次,发现了霍普夫分岔与混沌现象,并证明了其吸引子的存在性;最后,详细的数值结果展示了从分岔到混沌的全过程.
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.
王贺元;何香红
广东科技学院,广东 东莞 523083广东科技学院,广东 东莞 523083
数理科学
霍普夫分岔李雅普诺夫函数奇异吸引子
Hopf bifurcationLyapunov functionChaotic attractor
《应用数学》 2026 (3)
897-905,9
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)
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