Dynamical analysis of a new fractional-order Rabinovich system and its fractional matrix projective synchronization

被引:11
|
作者
He, Jinman [1 ]
Chen, Fangqi [2 ,3 ]
机构
[1] Nanjing Univ Aeronaut & Astronaut, Dept Mech, Nanjing 210016, Jiangsu, Peoples R China
[2] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Jiangsu, Peoples R China
[3] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China
基金
中国国家自然科学基金;
关键词
Fractional-order Rabinovich system; Chaotic attractors; Chaotic control; Fractional matrix projective synchronization; CHAOTIC SYSTEMS; HYPERCHAOTIC SYSTEMS; DIFFERENCE-EQUATIONS; STABILITY ANALYSIS; DELAY; UNCERTAINTIES;
D O I
10.1016/j.cjph.2018.09.014
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
This paper constructs a new physical system, i.e., the fractional-order Rabinovich system, and investigates its stability, chaotic behaviors, chaotic control and matrix projective synchronization. Firstly, two Lemmas of the new system's stability at three equilibrium points are given and proved. Next, the largest Lyapunov exponent, the corresponding bifurcation diagram and the chaotic behaviors are studied. Then, the linear and nonlinear feedback controllers are designed to realize the system's local asymptotical stability and the global asymptotical stability, respectively. It's particularly significant that, the fractional matrix projective synchronization between two Rabinovich systems is achieved and two kinds of proofs are provided for Theorem 4.1. Especially, under certain degenerative conditions, the fractional matrix projective synchronization can be reduced to the complete synchronization, anti-synchronization, projective synchronization and modified projective synchronization of the fractional-order Rabinovich systems. Finally, all the theoretical analysis is verified by numerical simulation.
引用
收藏
页码:2627 / 2637
页数:11
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