Chaos Synchronization of Hyperchaos Rossler System

2014 ◽  
Vol 687-691 ◽  
pp. 724-727
Author(s):  
Lin Wu ◽  
Jin Cheng Wei ◽  
Liu Jie
Keyword(s):  
Numerical Simulation ◽  
Chaos Synchronization ◽  
Simulation Experiment ◽  
Nonlinear Feedback ◽  
Driving System ◽  
Lyapunov Stabilization ◽  
Rossler System ◽  
Rössler System

Taking the hyperchaos Rossler system as an example and based on the Lyapunov Stabilization Law, with the parameters unknown, through the designing of controller, the synchronization of the driving system and the responding system has been realized by using the nonlinear feedback controlling method. This method provides a convenient way for the synchrocontrol of hyperchaos system, whose effectiveness has been further proved by the numerical simulation experiment.

Delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system

2016 ◽  
Vol 9 (2) ◽  
pp. 205-216 ◽  
Author(s):  
Ping He ◽  
Tao Fan
Keyword(s):  
Nonlinear Systems ◽  
Time Delays ◽  
Chaos Synchronization ◽  
Linear Matrix ◽  
Multiple Time ◽  
Content Type ◽  
Multiple Time Delays ◽  
Rossler System ◽  
Rössler System ◽  
And Algebra

Purpose – The purpose of this paper is with delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system. Design/methodology/approach – Based on linear matrix inequality and algebra Riccati matrix equation, the stabilization result is derived to guarantee asymptotically stable and applicated in chaos synchronization of Rössler chaotic system with multiple time-delays. Findings – A controller is designed and added to the nonlinear system with multiple time-delays. The stability of the nonlinear system at its zero equilibrium point is guaranteed by applying the appropriate controller signal based on linear matrix inequality and algebra Riccati matrix equation scheme. Another effective controller is also designed for the global asymptotic synchronization on the Rössler system based on the structure of delay-independent stabilization of nonlinear systems with multiple time-delays. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme. Originality/value – The introduced approach is interesting for delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

CHAOS SYNCHRONIZATION VIA CONTROLLING PARTIAL STATE OF CHAOTIC SYSTEMS

2001 ◽  
Vol 11 (06) ◽  
pp. 1737-1741 ◽  
Author(s):  
XINGHUO YU ◽  
YANXING SONG
Keyword(s):  
Invariant Manifold ◽  
Fourth Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Dynamic Properties ◽  
Rossler System ◽  
Rössler System ◽  
Partial State ◽  
The Lorenz System

An invariant manifold based chaos synchronization approach is proposed in this letter. A novel idea of using only a partial state of chaotic systems to synchronize the coupled chaotic systems is presented by taking into account the inherent dynamic properties of the chaotic systems. The effectiveness of the approach and idea is tested on the Lorenz system and the fourth-order Rossler system.

Chaos Synchronization Between Unified Chaotic System And Rossler System

2013 ◽  
Vol 321-324 ◽  
pp. 2464-2470
Author(s):  
Hao Wu ◽  
Bo Lun Xu ◽  
Chang Fan ◽  
Xian Yong Wu
Keyword(s):  
Active Control ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Adaptive Synchronization ◽  
System Parameters ◽  
Unified Chaotic System ◽  
Rossler System ◽  
Response Systems ◽  
Rössler System ◽  
Different Chaotic Systems

In this paper, two synchronization schemes between two different chaotic systems are proposed. Chaos synchronization between unified chaotic system and Rossler system via active control and adaptive control are investigated. Different controllers are designed to synchronize the drive and response systems. Active control synchronization is used when system parameters are known; adaptive synchronization is employed when system parameters are unknown or uncertain. Simulation results show the effectiveness of the proposed schemes.

HOPF BIFURCATION CONTROL USING NONLINEAR FEEDBACK WITH POLYNOMIAL FUNCTIONS

2004 ◽  
Vol 14 (05) ◽  
pp. 1683-1704 ◽  
Author(s):  
PEI YU ◽  
GUANRONG CHEN
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Control ◽  
Hopf Bifurcations ◽  
Nonlinear Feedback ◽  
Lorenz Equation ◽  
System A ◽  
Rossler System ◽  
Rössler System ◽  
The Lorenz System ◽  
The Stability

A general explicit formula is derived for controlling bifurcations using nonlinear state feedback. This method does not increase the dimension of the system, and can be used to either delay (or eliminate) existing bifurcations or change the stability of bifurcation solutions. The method is then employed for Hopf bifurcation control. The Lorenz equation and Rössler system are used to illustrate the application of the approach. It is shown that a simple control can be obtained to simultaneously stabilize two symmetrical equilibria of the Lorenz system, and keep the symmetry of Hopf bifurcations from the equilibria. For the Rössler system, a control is also obtained to simultaneously stabilize two nonsymmetric equilibria and meanwhile stabilize possible Hopf bifurcations from the equilibria. Computer simulation results are presented to confirm the analytical predictions.

scholarly journals Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

2021 ◽  
Vol 11 (15) ◽  
pp. 6955
Author(s):  
Andrzej Rysak ◽  
Magdalena Gregorczyk
Keyword(s):  
Optimal Parameter ◽  
Differential Transform Method ◽  
Bifurcation Diagrams ◽  
Transform Method ◽  
Rossler System ◽  
Differential Transform ◽  
Rössler System ◽  
Fractional System ◽  
Parameter Values

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

A SIMPLE OBSERVER OF THE HYPERCHAOTIC RÖSSLER SYSTEM

2010 ◽  
Vol 24 (22) ◽  
pp. 4325-4331
Author(s):  
XING-YUAN WANG ◽  
JUN-MEI SONG
Keyword(s):  
Dynamical System ◽  
Time Domain ◽  
Global Exponential Stability ◽  
Observer Design ◽  
The Other ◽  
State Observation ◽  
Rossler System ◽  
Error System ◽  
Rössler System ◽  
The Time Domain

This paper studies the hyperchaotic Rössler system and the state observation problem of such a system being investigated. Based on the time-domain approach, a simple observer for the hyperchaotic Rössler system is proposed to guarantee the global exponential stability of the resulting error system. The scheme is easy to implement and different from the other observer design that it does not need to transmit all signals of the dynamical system. It is proved theoretically, and numerical simulations show the effectiveness of the scheme finally.

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