NDLI: Typical complex behaviors induced by numerical algorithm in dynamical analysis of fractional order nonlinear systems

Content Provider	IEEE Xplore Digital Library
Author	Liu Jie Dong Pengzhen Shang Gang
Copyright Year	2010
Description	Author affiliation: Research Centre of Nonlinear Science, Wuhan University of Science and Engineering, 430073, China (Liu Jie; Dong Pengzhen; Shang Gang)
Abstract	Nowadays, identification, dynamical analysis, control and synchronization of fractional dynamical systems have become a focus topic in the nonlinear research fields. Researchers always us a linear time invariant transfer function (LTI) to approximate the fractional transfer function in related numerical investigation and then put their results into circuits designing, signal processing, etc. In this paper, we further carry out the investigation on the reliability of existed methods on this topic. Firstly, we discussed the serious topic via case study on the newly proposed Liu chaotic system and its commensurate fractional system. Our research reveals that, the most widely used Charef and Oustaloup methods may cause fake chaotic or fake periodic phenomena under some wrong conditions. That's to say, the traditional frequency method may be invalid under some situation. Then, it is suggested that the modified Oustaloup method can improve the reliability of the traditional frequency LTI method, since the modified method behaves much better on the left and right boundary of a related interval of fitting. By using such a new method, possible cases of fake complex phenomena caused by traditional LTI methods might be avoided successfully. Lastly, it is also addressed that the ADM predictor-corrector scheme may also cause fake complex behaviors while using unsuitable length of iteration step by taking the hyper-chaotic system as illustrations. So, it is suggested that, the modified frequency approximate method is more suitable for numerical analysis for the case which is far from the transient state boundary between order and chaos. While using the ADM predictor-corrector scheme, smaller iteration step should be used for avoiding fake chaos. Numerical analysis further confirmed our analysis.
Starting Page	775
Ending Page	780
File Size	1496077
Page Count	6
File Format	PDF
ISBN	9781424462636
e-ISBN	9787894631046
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-07-29
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Chinese Association of Aut
Subject Keyword	Chaos Stability Analysis Simulation Stability criteria ADM Predictor-corrector Scheme Fractional Chaotic System Transfer functions Fake Chaos Eigenvalues and eigenfunctions Approximation methods Modified Oustaloup Approximate Method
Content Type	Text
Resource Type	Article

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