CHAOTIC SYNCHRONIZATION OF FRACTIONAL-ORDER MODIFIED COUPLED DYNAMOS SYSTEM

2009 ◽  
Vol 23 (31) ◽  
pp. 5769-5777 ◽  
Author(s):  
XINGYUAN WANG ◽  
YIJIE HE
Keyword(s):  
Fractional Order ◽  
Lorenz System ◽  
Chaotic Synchronization ◽  
The Self ◽  
Simulation Results ◽  
System Designs

This paper studies the problem of chaotic synchronization of the fractional-order modified coupled dynamos system, designs the activate controllers, and then proves that the self-synchronization of the fractional-order modified coupled dynamos system and the fractional-order modified coupled dynamos system's different structure synchronization with the fractional-order Lorenz system can both arrive theoretically. The simulation results demonstrate the validity of the activate controller.

CHAOTIC SYNCHRONIZATION OF FRACTIONAL-ORDER SPATIOTEMPORAL COUPLED LORENZ SYSTEM

2012 ◽  
Vol 23 (10) ◽  
pp. 1250067 ◽  
Author(s):  
XING-YUAN WANG ◽  
HAO ZHANG
Keyword(s):  
Fractional Order ◽  
Chaos Theory ◽  
Lorenz System ◽  
Systems Design ◽  
Lyapunov Stability Theory ◽  
Chaotic Synchronization ◽  
Spatiotemporal Chaos ◽  
Nonlinear Controller ◽  
Simulation Results ◽  
First Time

By utilizing the fractional calculus techniques and spatiotemporal chaos theory, this paper brings Lorenz system to fractional-order spatiotemporal coupled differential equation for the first time, and proposes the fractional-order spatiotemporal coupled Lorenz system. Based on that, we study the problem of chaotic synchronization of fractional-order spatiotemporal coupled Lorenz systems, design the linear controller and nonlinear controller by utilizing the Lyapunov stability theory and prove the correctness in theory. The numerical simulation results demonstrate the validity of controllers in high-dimension fractional-order spatiotemporal coupled Lorenz system.

ACTIVE TRACKING CONTROL OF THE HYPERCHAOTIC LORENZ SYSTEM

2008 ◽  
Vol 22 (19) ◽  
pp. 1859-1865 ◽  
Author(s):  
XINGYUAN WANG ◽  
DAHAI NIU ◽  
MINGJUN WANG
Keyword(s):  
Numerical Simulation ◽  
Tracking Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
The Self ◽  
Hyperchaotic System ◽  
Reference Signals ◽  
Tracking Controller ◽  
Hyperchaotic Lorenz System ◽  
Simulation Results

A nonlinear active tracking controller for the four-dimensional hyperchaotic Lorenz system is designed in the paper. The controller enables this hyperchaotic system to track all kinds of reference signals, such as the sinusoidal signal. The self-synchronization of the hyperchaotic Lorenz system and the different-structure synchronization with other chaotic systems can also be realized. Numerical simulation results show the effectiveness of the controller.

CHAOS IN DIFFUSIONLESS LORENZ SYSTEM WITH A FRACTIONAL ORDER AND ITS CONTROL

2012 ◽  
Vol 22 (04) ◽  
pp. 1250088 ◽  
Author(s):  
YONG XU ◽  
RENCAI GU ◽  
HUIQING ZHANG ◽  
DONGXI LI
Keyword(s):  
Feedback Control ◽  
Control Problem ◽  
Fractional Order ◽  
Lorenz System ◽  
Equilibrium Points ◽  
Control Technique ◽  
Order System ◽  
System Parameters ◽  
Simulation Results ◽  
The Stability

This paper aims to investigate the phenomenon of Diffusionless Lorenz system with fractional-order. We discuss the stability of equilibrium points of the fractional-order system theoretically, and analyze the chaotic behaviors and typical bifurcations numerically. We find rich dynamics in fractional-order Diffusionless Lorenz system with appropriate fractional order and system parameters. Besides, the control problem of fractional-order Diffusionless Lorenz system is examined using feedback control technique, and simulation results show the effectiveness of the method.

Bivariate Module-Phase Synchronization of a Fractional-Order Lorenz System in Different Dimensions

2013 ◽  
Vol 8 (3) ◽  
Author(s):  
Xing-Yuan Wang ◽  
Hao Zhang
Keyword(s):  
Numerical Simulation ◽  
Phase Space ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Lorenz System ◽  
Phase Synchronization ◽  
High Dimensional ◽  
Different Dimensions ◽  
Simulation Results ◽  
First Time

Based on the classic Lorenz system, this paper studies the problem of bivariate module-phase synchronizations in a fractional-order Lorenz system, bivariate module-phase synchronizations in a fractional-order spatiotemporal coupled Lorenz system, and malposed module-phase synchronization in a fractional-order spatiotemporal coupled Lorenz system. It is the first time, to our knowledge, that module-phase synchronization in fractional-order high-dimensional systems is applied. According to the fractional calculus techniques and spatiotemporal theory, we design controllers and achieve synchronizations both in module space and phase space at the same time. In the simulation, we discuss the bivariate module-phase synchronization and malposed module-phase synchronization. The numerical simulation results demonstrate the validity of controllers.

GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER HYPERCHAOTIC LORENZ SYSTEM

2009 ◽  
Vol 23 (17) ◽  
pp. 2167-2178 ◽  
Author(s):  
TIANSHU WANG ◽  
XINGYUAN WANG
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Lorenz System ◽  
Order System ◽  
Generalized Synchronization ◽  
Response System ◽  
Hyperchaotic Lorenz System ◽  
Simulation Results ◽  
The Stability ◽  
Predictor Corrector

In this paper, a type of new fractional order hyperchaotic Lorenz system is proposed. Based on the fractional calculus predictor-corrector algorithm, the fractional order hyperchaotic Lorenz system is investigated numerically, and the simulation results show that the lowest orders for hyperchaos in hyperchaotic Lorenz system is 3.884. According to the stability theory of fractional order system, an improved state-observer is designed, and the response system of generalized synchronization is obtained analytically, whose feasibility is proved theoretically. The synchronization method is adopted to realize the generalized synchronization of 3.884-order hyperchaotic Lorenz system, and the numerical simulation results verify the effectiveness.

scholarly journals The Synchronization Behaviors of Coupled Fractional-Order Neuronal Networks under Electromagnetic Radiation

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2204
Author(s):  
Xin Yang ◽  
Guangjun Zhang ◽  
Xueren Li ◽  
Dong Wang
Keyword(s):  
Electromagnetic Radiation ◽  
Fractional Order ◽  
Neuronal Network ◽  
Neuronal Networks ◽  
Phase Synchronization ◽  
Chaotic Synchronization ◽  
Feedback Gain ◽  
Integer Order ◽  
Conductance Parameter ◽  
Simulation Results

Previous studies on the synchronization behaviors of neuronal networks were constructed by integer-order neuronal models. In contrast, this paper proposes that the above topics of symmetrical neuronal networks are constructed by fractional-order Hindmarsh–Rose (HR) models under electromagnetic radiation. They are then investigated numerically. From the research results, several novel phenomena and conclusions can be drawn. First, for the two symmetrical coupled neuronal models, the synchronization degree is influenced by the fractional-order q and the feedback gain parameter k1. In addition, the fractional-order or the parameter k1 can induce the synchronization transitions of bursting synchronization, perfect synchronization and phase synchronization. For perfect synchronization, the synchronization transitions of chaotic synchronization and periodic synchronization induced by q or parameter k1 are also observed. In particular, when the fractional-order is small, such as 0.6, the synchronization transitions are more complex. Then, for a symmetrical ring neuronal network under electromagnetic radiation, with the change in the memory-conductance parameter β of the electromagnetic radiation, k1 and q, compared with the fractional-order HR model’s ring neuronal network without electromagnetic radiation, the synchronization behaviors are more complex. According to the simulation results, the influence of k1 and q can be summarized into three cases: β>0.02, −0.06<β<0.02 and β<−0.06. The influence rules and some interesting phenomena are investigated.

scholarly journals An Intelligent Evaluation Method to Analyze the Competitiveness of Airlines

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Jun Zhao ◽  
Xumei Chen
Keyword(s):  
Neural Network ◽  
Prior Knowledge ◽  
Evaluation Method ◽  
Standard Sample ◽  
Reference Value ◽  
The Self ◽  
Index Data ◽  
Som Neural Network ◽  
Simulation Results ◽  
Self Organizing

An intelligent evaluation method is presented to analyze the competitiveness of airlines. From the perspective of safety, service, and normality, we establish the competitiveness indexes of traffic rights and the standard sample base. The self-organizing mapping (SOM) neural network is utilized to self-organize and self-learn the samples in the state of no supervision and prior knowledge. The training steps of high convergence speed and high clustering accuracy are determined based on the multistep setting. The typical airlines index data are utilized to verify the effect of the self-organizing mapping neural network on the airline competitiveness analysis. The simulation results show that the self-organizing mapping neural network can accurately and effectively classify and evaluate the competitiveness of airlines, and the results have important reference value for the allocation of traffic rights resources.

scholarly journals Realization of a fractional-order RLC circuit via constant phase element

2021 ◽  
Author(s):  
Riccardo Caponetto ◽  
Salvatore Graziani ◽  
Emanuele Murgano
Keyword(s):  
Experimental Data ◽  
Carbon Black ◽  
Fractional Order ◽  
Constant Phase Element ◽  
Polymeric Matrix ◽  
Fractional Order Systems ◽  
New Device ◽  
Rlc Circuit ◽  
Simulation Results

AbstractIn the paper, a fractional-order RLC circuit is presented. The circuit is realized by using a fractional-order capacitor. This is realized by using carbon black dispersed in a polymeric matrix. Simulation results are compared with the experimental data, confirming the suitability of applying this new device in the circuital implementation of fractional-order systems.

CHAOS SYNCHRONIZATION VIA UNIDIRECTIONAL COUPLING AND ITS APPLICATION TO SECURE COMMUNICATION

2009 ◽  
Vol 23 (32) ◽  
pp. 5949-5964 ◽  
Author(s):  
XINGYUAN WANG ◽  
MINGJUN WANG
Keyword(s):  
Secure Communication ◽  
Chaos Synchronization ◽  
Function Method ◽  
The Self ◽  
Largest Lyapunov Exponent ◽  
Global Synchronization ◽  
Unidirectional Coupling ◽  
Response System ◽  
Lyapunov Function Method ◽  
Simulation Results

This paper studies chaos synchronization via unidirectional coupling. The self-synchronization of Lorenz systems, modified coupled dynamos systems and hyperchaotic Chen systems is studied by three methods: the Lyapunov function method, the global synchronization method and the numerical calculation of the largest Lyapunov exponent method. In regard to application to communication, we show that via transmitting single signal the synchronization of the drive system and the response system can be achieved. An example of applying self-synchronization of hyperchaotic Chen systems to chaotic masking secure communication is presented in this paper. Simulation results show the effectiveness of the method.

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

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