频域法在分数阶混沌系统计算中的局限性分析

王茂, 孙光辉, 魏延岭

哈尔滨工业大学空间控制与惯性技术研究中心



摘要:

基于分数阶积分算子在频域内的响应,分析了频域近似法在分数阶混沌系统计算中的局限性.频域近似法只能在期望的频带范围内实现与实际系统的近似,而在高频与低频段都存在着较大的误差.因此,当其应用到分数阶混沌系统计算时存在着很大的局限性,甚至得到与预估-校正算法完全不同的结论.通过对分数阶Chen系统的仿真,验证了该结论的正确性.

关键词:  频域近似法  预估-校正算法  分数阶系统  混沌系统

DOI：10.11918/j.issn.0367-6234.2011.05.002

分类号:O415.5

基金项目:国家自然科学基金资助项目(60804002)



Limitations of frequency domain approximation in the calculation of fractional order chaotic systems

WANG Mao, SUN Guang-hui, WEI Yan-ling

Space Control and Inertial Technology Research Center,Harbin Institute of Technology,150080 Harbin,China

Abstract:

Based on the frequency response of the fractional integral operator,this work analyses the limitations of frequency domain approximation algorithm in the calculation of fractional order chaotic systems.The frequency domain approximation algorithm can approach to the original system in desired frequency band,but in the low and high frequency band there are large errors.Therefore,there are some limitations in the calculation of fractional chaotic system.Comparing with the predictor-corrector algorithm,totally different conclusions can be got by the frequency domain approximation algorithm.Taking the fractional Chen system as an example,numerical simulation results verify the effectiveness of our results.

Key words:  frequency domain approximation  predictor-corrector algorithm  fractional-order system  chaotic system