Fractional-Order Hidden Attractor Based on the Extended Liu System
Joint Authors
Wang, Yaoyu
Cai, Xinshan
Wang, Yan
Zheng, Guangchao
Liu, Ling
Chong-xin, Liu
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-08-04
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
In this paper, a new commensurate fractional-order chaotic oscillator is presented.
The mathematical model with a weak feedback term, which is named hypogenetic flow, is proposed based on the Liu system.
And with changing the parameters of the system, the hidden attractor can have no equilibrium points or line equilibrium.
What is more interesting is that under the occasion that no equilibrium point can be obtained, the phase trajectory can converge to a minimal field under the lead of some initial conditions, similar to the fixed point.
We call it the virtual equilibrium point.
On the other hand, when the value of parameters can produce an infinite number of equilibrium points, the line equilibrium points are nonhyperbolic.
Moreover than that, there are coexistence attractors, which can present hyperchaos, chaos, period, and virtual equilibrium point.
The dynamic characteristics of the system are analyzed, and the parameter estimation is also studied.
Then, an electronic circuit implementation of the system is built, which shows the feasibility of the system.
At last, for the fractional system with hidden attractors, the finite-time synchronization control of the system is carried out based on the finite-time stability theory of the fractional system.
And the effectiveness of the controller is verified by numerical simulation.
American Psychological Association (APA)
Wang, Yaoyu& Liu, Ling& Cai, Xinshan& Chong-xin, Liu& Wang, Yan& Zheng, Guangchao. 2020. Fractional-Order Hidden Attractor Based on the Extended Liu System. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-22.
https://search.emarefa.net/detail/BIM-1193216
Modern Language Association (MLA)
Wang, Yaoyu…[et al.]. Fractional-Order Hidden Attractor Based on the Extended Liu System. Mathematical Problems in Engineering No. 2020 (2020), pp.1-22.
https://search.emarefa.net/detail/BIM-1193216
American Medical Association (AMA)
Wang, Yaoyu& Liu, Ling& Cai, Xinshan& Chong-xin, Liu& Wang, Yan& Zheng, Guangchao. Fractional-Order Hidden Attractor Based on the Extended Liu System. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-22.
https://search.emarefa.net/detail/BIM-1193216
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1193216