Rikitake双圆盘耦合发电机系统的动力学行为仿真与分析

推导出了Rikitake双圆盘耦合发电机系统的数学方程,明确了在不同参数下发电机电流与圆盘角速度的关系,计算了李雅普诺夫指数及混沌吸引子的分维数.讨论了系统的混沌分岔行为和周期窗口的性态变化及其可能出现的混沌运动形态,数值仿真得到双圆盘发电机模型在一定参数和初始状态下的混沌吸引子,并分析了系统的对称性、平衡点、功率谱及稳定性等基本动力学特性.这些特性在机电控制等方面具有重要的理论意义和实用价值,也为解释地磁场逆转问题提供新的思路.

Dynamic Behavior Simulation and Analysis of the Rikitake Two-disk Dynamo System

The mathematical equations of the Rikitake two-disk dynamo have been derived.The relationship between the dynamo currents and the angular velocity of disk has been defined.It calculated the lyapunov exponent and fractal dimension of chaotic attractor.And then this paper discussed the system’s chaotic bifurcation behavior and the state diversification of its periodical windows,as well might appear chaotic movement patterns.After simulating,it obtained the Rikitake two-disk dynamo’s chaotic attractors.Moreover,it analyzed the system’s basic dynamic behavior such as symmetry,power spectrum,equilibrium pots,stability and so on.These chaotic behavior can be used to simulate the reversals of the geomagnetic field.Furthermore,it has important theory significance and practical value.