Rikitake双盘发电机模型的混沌行为分析与数值仿真

Chaotic Behavior Analysis and Numerical Simulation of Rikitake Two-Disk Generator Model

摘要: 通过混沌理论分析和数值仿真方法，对Rikitake双盘发电机模型的混沌行为进行讨论。将Rikitake双盘发电机模型无量纲方程写成三维常系数微分方程组，讨论该系统的耗散性、吸引子的存在性、系统的对称性和不变性。计算系统的平衡点，讨论平衡点的局部稳定性。通过MATLAB编程，从分岔图、最大Lyapunov指数图、吸引子图、时间序列、功率谱等指标分析系统的混沌现象。

Abstract: Through chaos theory analysis and numerical simulation, the chaotic behavior of Rikitake’s two-disk generator model is discussed. The dimensionless equation of Rikitake’s two-disk generator model is written into three-dimensional constant coefficient differential equations, and the dissipation, the existence of attractors, the symmetry and invariance of the system are discussed. The equilibrium point of the system is calculated and the local stability of the equilibrium point is discussed. MATLAB programming was used to analyze the chaotic phenomenon of the system from the bifurcation graph, maximum Lyapunov index graph, attractor graph, time series, power spectrum and other indicators.