一个新分数阶混沌系统的分析与同步

Analysis and Synchronization of a Novel Fractional-order Chaotic System

提出一个新的同量阶2.7阶分数阶混沌系统,基于预估-校正时域法,采用Matlab绘制了该分数阶混沌系统的相轨迹图、Lyapunov指数图和分岔图,并用数值仿真验证了该系统在一定参数变化范围内存在混沌吸引子.研究该分数阶混沌系统的同步问题,基于极点配置方法以及扩展的非线性状态观测器理论,设计了一种投影同步方案.数值仿真与理论分析的结果一致,充分验证了该同步方案的可行性和有效性.

In this research, a novel commensurate 2.7-order fractional-order chaotic system is proposed. The phase trajectory diagrams, the Lyapunov exponent spectra, and the bifurcation diagrams of the fractional-order chaotic system were establisher by using Matlab software and based on the predictor-corrector time domain method. The results imply there exists a chaotic attractor in the system with a certain range of change in system parameters. On this basis, the synchronization of the fractional-order chaotic system was investigated and a projection synchronization scheme based on the pole assignment method and the extended nonlinear state observer theory was designed. The simulation results are consistent with the theoretical analysis, which fiLrther demonstrates the feasibility and effectiveness of the proposed synchronization scheme.