摘要
基于波特图的频域近似方法,研究了分数阶Lü混沌系统.从系统的分岔图、Lyapunov指数图和吸引子相位图等数值仿真分析验证了不同阶次Lü混沌系统丰富的动力学特性.又基于该方法和整数阶混沌电路的设计方法,设计了模拟电路,实现了该分数阶Lü系统,电路中的电阻和电容等数值是由系统参数和频域传递函数近似确定的.最后,观测示波器电路实验结果与理论分析结果相一致,从而进一步揭示了混沌系统的可实现性与动力学特性.
In this paper,fractional order Lü chaotic system is studied based on approximate method in frequency domain of the Potter chart.The rich characteristics of different order Lüchaotic systems are ana-lyzed and validated according to the numerical simulation analysis of the system bifurcation diagram,Lya-punov diagram and phase diagram of exponential attractor.Besides,the circuit is designed to realize the fractional-order Lü system based on this method and the method used in the integer order chaotic circuits. The values of the resistors and capacitors in the circuit are selected according to the system parameters and transfer function approximation in frequency domain.The experimental results are consistent with the nu-merical calculation through the oscilloscope observation,which reveals the abundant dynamics characteris-tic and realization of the chaotic system to the further.
出处
《曲阜师范大学学报（自然科学版）》
CAS
2015年第2期35-41,共7页
Journal of Qufu Normal University(Natural Science)
基金
陕西省教育厅科研计划项目(2013JK1068)
西京学院科研基金(XJ130117)
