Global dynamics of fractional-order systems with an extended generalized cell mapping method

被引：0
作者：
Xiaojun Liu
Ling Hong
Jun Jiang
Dafeng Tang
Lixin Yang
机构：
[1] Xi’an Jiaotong University,State Key Laboratory for Strength and Vibration of Mechanical Structures
[2] Tianshui Normal University,School of Mathematics and Statistics
来源：
Nonlinear Dynamics | 2016年 / 83卷
关键词：
Fractional-order systems; Short memory principle; Generalized cell mapping; Global dynamics; Predictor–corrector method;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Global dynamics of fractional-order systems is studied with an extended generalized cell mapping (EGCM) method. The one-step transition probability matrix of Markov chain of the EGCM is generated by means of the improved predictor–corrector approach for fractional-order systems. The one-step mapping time of the proposed method is evaluated with the help of the short memory principle for fractional derivatives to deal with its non-local property and to properly define a bound of the truncation error and a function M by considering the features of cell mapping. In this way, a method of generalized cell mapping for global dynamics of a fractional-order system is developed. Three examples of global analysis on fractional-order systems are given to demonstrate the validity and efficiency of the proposed method. And attractors, boundaries, basins of attraction, and saddles are obtained by the EGCM.
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页码：1419 / 1428
页数：9
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