Fixed-Time Complex Modified Function Projective Lag Synchronization of Chaotic (Hyperchaotic) Complex Systems

Tran, Xuan-Toa; Kang, Hyejin

doi:10.1155/2017/4020548

Cited by 8 publications

(4 citation statements)

References 29 publications

(71 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Definition 1 [39]: The equilibrium point of Eq. ( 1) is considered to be globally finite-time stable in case it is globally asymptotically stable and any solution x(t, x 0 ) of Eq.…”

Section: Preliminaries and Problem Presentation A Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Complex Modified Function Projective Lag Synchronization With Fixed-Time Stability Guarantees for Hyperchaotic Systems via a Fixed-Time Control Proposal

Truong

Kang

2022

IEEE Access

View full text Add to dashboard Cite

Our paper investigates complex modified function projective lag synchronization with fixed-time stability guarantees for hyperchaotic systems via a FxTC proposal. The synchronization of complex hyperchaotic systems and the desired performance are definitely guaranteed within a period of bounded time. The synchronization interval can be predefined without demanding the information of the initial conditions from the systems where the synchronization is performed. Furthermore, the fixed-time stability guarantees of the control scheme are achieved according to the Lyapunov principle and the settling time is calculated by solving the differential equations. In MATLAB/SIMULINK environment, synchronization performance from two simulation examples is performed in many cases with the change of initial values and time delay of the system to reveal the feasibility and the efficacy of the control proposal.INDEX TERMS Fixed-time control theory, hyperchaotic complex systems, complex modified function projective lag synchronization. HEE-JUN KANG received the Bachelor of Science degree in mechanical engineering from Seoul National University, South Korea, in 1985, and the Master of Science and Doctor of Philosophy degrees in mechanical engineering from The University of Texas at Austin, USA, in 1988 and 1991, respectively. He joined the University of Ulsan, in 1992, where he is currently a Professor of electrical engineering. In addition to sensorbased robotics, haptics, robot fault diagnosis, and mechanisms analysis, his current research interests include encompass robot calibration, robot calibration, haptics, and mechanism analysis.

show abstract

“…Definition 1 [39]: The equilibrium point of Eq. ( 1) is considered to be globally finite-time stable in case it is globally asymptotically stable and any solution x(t, x 0 ) of Eq.…”

Section: Preliminaries and Problem Presentation A Preliminariesmentioning

confidence: 99%

“…Definition 2 [39]: The equilibrium point of Eq. ( 1) is considered to be a fixed-time stable equilibrium point in case it also is globally finite-time stable within bounded settling-time function T (x 0 ), i.e.…”

Section: Preliminaries and Problem Presentation A Preliminariesmentioning

confidence: 99%

Complex Modified Function Projective Lag Synchronization With Fixed-Time Stability Guarantees for Hyperchaotic Systems via a Fixed-Time Control Proposal

Truong

Kang

2022

IEEE Access

View full text Add to dashboard Cite

show abstract

“…is pioneering work greatly promoted the study of chaotic synchronization theory. Since then, complete synchronization [74], antisynchronization [40], generalized synchronization [75], projection synchronization [76,77], lag synchronization [78], function projection synchronization [79], and shape synchronization [80] methods have been widely studied in the literature.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis, Circuit Design, and Synchronization of a Novel 6D Memristive Four-Wing Hyperchaotic System with Multiple Coexisting Attractors

Liu

Shen

et al. 2020

Complexity

View full text Add to dashboard Cite

In this work, a novel 6D four-wing hyperchaotic system with a line equilibrium based on a flux-controlled memristor model is proposed. The novel system is inspired from an existing 5D four-wing hyperchaotic system introduced by Zarei (2015). Fundamental properties of the novel system are discussed, and its complex behaviors are characterized using phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy. When a suitable set of parameters are chosen, the system exhibits a rich repertoire of dynamic behaviors including double-period bifurcation of the quasiperiod, a single two-wing, and four-wing chaotic attractors. Further analysis of the novel system shows that the multiple coexisting attractors can be observed with different system parameter values and initial values. Moreover, the feasibility of the proposed mathematical model is also presented by using Multisim simulations based on an electronic analog of the model. Finally, the active control method is used to design the appropriate controller to realize the synchronization between the proposed 6D memristive hyperchaotic system and the 6D hyperchaotic Yang system with different structures. The Routh–Hurwitz criterion is used to prove the rationality of the controller, and the feasibility and effectiveness of the proposed synchronization method are proved by numerical simulations.

show abstract

“…The various methods of chaos control have been put forward by researchers [11][12][13][14][15][16]; these control methods were mostly based on infinite time control. In fact, complex systems are usually required to be controlled in a certain amount of time, the finite time control became an important index to measure the quality of the control criteria, and it not only has important theoretical significance and also has important practical value [17].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Evolution Analysis of Stock Price Fluctuation and Its Control

Xie

et al. 2018

Complexity

View full text Add to dashboard Cite

This paper studies a simple dynamical system of stock price fluctuation time series based on the rule of stock market. When the stock price fluctuation system is disturbed by external excitations, the system exhibits obviously chaotic phenomena, and its basic dynamic properties are analyzed. At the same time, a new fixed-time convergence theorem is proposed for achieving fixed-time control of stock price fluctuation system. Finally, the effectiveness of the method is verified by numerical simulation.

show abstract

Fixed-Time Complex Modified Function Projective Lag Synchronization of Chaotic (Hyperchaotic) Complex Systems

Cited by 8 publications

References 29 publications

Complex Modified Function Projective Lag Synchronization With Fixed-Time Stability Guarantees for Hyperchaotic Systems via a Fixed-Time Control Proposal

Complex Modified Function Projective Lag Synchronization With Fixed-Time Stability Guarantees for Hyperchaotic Systems via a Fixed-Time Control Proposal

Dynamic Analysis, Circuit Design, and Synchronization of a Novel 6D Memristive Four-Wing Hyperchaotic System with Multiple Coexisting Attractors

Dynamic Evolution Analysis of Stock Price Fluctuation and Its Control

Contact Info

Product

Resources

About