CHAOS AND ADAPTIVE SYNCHRONIZATIONS IN FRACTIONAL-ORDER SYSTEMS

被引：7
作者：
Liu, Xiaojun [1 ]
Hong, Ling [1 ]
机构：
[1] Xi An Jiao Tong Univ, State Key Lab Strength & Vibrat Mech Struct, Xian 710049, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2013年 / 23卷 / 11期
基金：
中国国家自然科学基金;
关键词：
Chaos; synchronization; fractional-order systems; bifurcation; GENESIO-TESI SYSTEMS; FEEDBACK-CONTROL; CHUAS SYSTEM; DYNAMICS;
D O I：
10.1142/S0218127413501757
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, chaos and adaptive synchronization for a fractional-order Genesio-Tesi system with fifth order nonlinearity are investigated. The minimum effective dimension for the system to remain chaotic is 2.784 in the commensurate-order case and 2.793 in the incommensurate-order case. A period-doubling bifurcation and an interior crisis from single-scroll to double-scroll attractors are also found with the variation of derivative order. Furthermore, based on the stability theory of fractional-order systems, the adaptive synchronization of the system with unknown parameters is realized by designing appropriated controllers. Numerical simulations are carried out to demonstrate the effectiveness and flexibility of the controllers.
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页数：12
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