Projective synchronization of new hyperchaotic system with fully unknown parameters

2009 ◽  
Vol 61 (1-2) ◽  
pp. 11-21 ◽  
Author(s):  
Dibakar Ghosh ◽  
Sikha Bhattacharya
Keyword(s):  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
New Hyperchaotic System

FUNCTION PROJECTIVE SYNCHRONIZATION OF THE CHAOTIC SYSTEMS WITH PARAMETERS UNKNOWN

2013 ◽  
Vol 27 (21) ◽  
pp. 1350110
Author(s):  
JIAKUN ZHAO ◽  
YING WU
Keyword(s):  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Parameter Update Law ◽  
Different Chaotic Systems ◽  
Hyperchaotic Systems ◽  
Adaptive Control Law

This work is concerned with the general methods for the function projective synchronization (FPS) of chaotic (or hyperchaotic) systems. The aim is to investigate the FPS of different chaotic (hyper-chaotic) systems with unknown parameters. The adaptive control law and the parameter update law are derived to make the states of two different chaotic systems asymptotically synchronized up to a desired scaling function by Lyapunov stability theory. The general approach for FPS of Chen hyperchaotic system and Lü system is provided. Numerical simulations are also presented to verify the effectiveness of the proposed scheme.

scholarly journals Modified Function Projective Synchronization of Fractional Order Chaotic Systems with Different Dimensions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hong-Juan Liu ◽  
Zhi-Liang Zhu ◽  
Hai Yu ◽  
Qian Zhu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Adaptive Controllers ◽  
Function Projective Synchronization ◽  
Modified Function Projective Synchronization ◽  
Different Dimensions ◽  
The Stability

The modified function projective synchronization of different dimensional fractional-order chaotic systems with known or unknown parameters is investigated in this paper. Based on the stability theorem of linear fractional-order systems, the adaptive controllers with corresponding parameter update laws for achieving the synchronization are given. The fractional-order chaotic system and hyperchaotic system are applied to achieve synchronization in both reduced order and increased order. The corresponding numerical results coincide with theoretical analysis.

Hybrid Projective Synchronization of a New Hyperchaotic System

2010 ◽  
Vol 42 ◽  
pp. 63-67
Author(s):  
Jie Fang ◽  
Xiao Ming Zhang ◽  
Chang Sheng Jiang
Keyword(s):  
Numerical Simulation ◽  
Chaos Synchronization ◽  
Projective Synchronization ◽  
Practical Significance ◽  
Hyperchaotic System ◽  
Complete Synchronization ◽  
Full State ◽  
Hybrid Projective Synchronization ◽  
The Stability ◽  
New Hyperchaotic System

The full state hybrid projective synchronization, which includes complete synchronization, anti-synchronization and projective synchronization as its special item, is a novel type of chaos synchronization, so the research in this area has high practical significance. This paper is involved with full state hybrid projective synchronization of a new hyperchaotic system. Based on the stability criterion of linear system, full state hybrid projective synchronization is achieved by appropriate linear separation. Numerical simulation is presented to demonstrate the effectiveness of the proposed method.

scholarly journals Projective synchronization for 4D hyperchaotic system based on adaptive nonlinear control strategy

2020 ◽  
Vol 19 (2) ◽  
pp. 715 ◽  
Author(s):  
Zaidoon Sh. Al-Talib ◽  
Saad Fawzi AL-Azzawi
Keyword(s):  
Nonlinear Control ◽  
Control Strategy ◽  
Chaotic Oscillation ◽  
Positive Definite Matrix ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Nonlinear Controller ◽  
Unknown Parameters ◽  
Nonlinear Controllers

<span>The main purpose of the paper is to projective synchronous chaotic oscillation in the real four-dimensional hyperchaotic model via designing many adaptive nonlinear controllers. Firstly, in view that there are many strategies in the design process of existing controllers, a nonlinear control strategy is considered as one of the important powerful tools for controlling the dynamical systems. The prominent advantage of the nonlinear controller lies in that it deals with known and unknown parameters. Then, the projective synchronize behavior of a four-dimensional hyperchaotic system is analyzed by using the Lyapunov stability theory and positive definite matrix, and the nonlinear control strategy is adopted to synchronize the hyperchaotic system. Finally, the effectiveness and robustness of the designed adaptive nonlinear controller are verified by simulation.</span>

scholarly journals A novel 4 dimensional hyperchaotic system with its control, Synchronization and Implementation

2021 ◽  
Vol 11 (4) ◽  
pp. 2974
Author(s):  
Basil H. Jasim ◽  
Anwer Hammadi Mjily ◽  
Anwer Mossa Jassim AL-Aaragee
Keyword(s):  
Numerical Analysis ◽  
Initial Conditions ◽  
Design Procedure ◽  
Hyperchaotic System ◽  
Matlab Simulation ◽  
Lyapunov Dimension ◽  
Unknown Parameters ◽  
Control And Synchronization ◽  
Microcontroller Unit ◽  
New Hyperchaotic System

This paper presents a new hyperchaotic system which shows some interesting features, the system is 4-dimensional with 4 nonlinearities. An extensive numerical analysis has showed that the system has some interesting features and strange behaviors. The numerical analysis includes studying the effect of system parameters and initial conditions. Some of the important properties of the system with parameter set, in which the system is hyperchaotic, such as Lyapunov exponents and Lyapunov dimension, dissipation and symmetry are found and discussed. In the next part of our work, a tracking controller for the proposed system is designed and then a synchronization control system for two identical systems is designed. The design procedure uses combination of a simple synergetic control with adaptive updating laws to identify the unknown parameters derived basing on Lyapunov theorem. Hardware implementation based on microcontroller unit (MCU) board is proposed and tested and used to experimentally validate the designed control and synchronization systems. As an application, the designed synchronization system is used as a secure analogue communication system. Using MATLAB, Simulation study for the control and synchronization systems is presented. The simulation and experimental study have been showed excellent results.

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