Projective Synchronization of a Modified Coupled Dynamos System

2012 ◽  
Vol 466-467 ◽  
pp. 1261-1265
Author(s):  
Chun Mei Wang ◽  
Ren Long Chang
Keyword(s):  
Chaotic System ◽  
Design Procedure ◽  
Scaling Factor ◽  
Drive System ◽  
Observer Design ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Systematic Design ◽  
Unified Chaotic System ◽  
Placement Technique

Based on techniques from the state observer design and the pole placement technique, we present a systematic design procedure to synchronize a modified coupled dynamos system by a scaling factor ( projective synchronization ). Compared with the method proposed by Wen and Xu, this method eliminates the nonlinear item from the output of the drive system. Furthermore, the scaling factor can be adjusted arbitrarily in due course of control without degrading the controllability. Finally, feasibility of the technique is illustrated for the unified chaotic system.

PROJECTIVE SYNCHRONIZATION OF A CLASS OF CHAOTIC SYSTEMS BASED ON OBSERVER

2011 ◽  
Vol 25 (28) ◽  
pp. 3765-3771 ◽  
Author(s):  
XING-YUAN WANG ◽  
XIN-GUANG LI
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Design Procedure ◽  
Scaling Factor ◽  
Observer Design ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Systematic Design ◽  
Unified Chaotic System ◽  
Placement Technique

Based on techniques from the state observer design and the pole placement technique, we present a systematic design procedure to synchronize a class of chaotic systems by a scaling factor (projective synchronization). Compared with the method proposed by Wen and Xu, this method eliminates the nonlinear item from the output of the drive system. Furthermore, the scaling factor can be adjusted arbitrarily in due course of control without degrading the controllability. Finally, feasibility of the technique is illustrated for the unified chaotic system.

Observe-Based Projective Synchronization of Chaotic Complex Modified Van Der Pol-Duffing Oscillator With Application to Secure Communication

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Ping Liu ◽  
Hongjun Song ◽  
Xiang Li
Keyword(s):  
Secure Communication ◽  
Chaotic Behavior ◽  
Design Method ◽  
Duffing Oscillator ◽  
Scaling Factor ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Projective Synchronization ◽  
Chaotic Oscillator ◽  
Van Der Pol

This paper addresses the projective synchronization (PS) of the complex modified Van der Pol-Duffing (MVDPD for short) chaotic oscillator by using the nonlinear observer control and also discusses its applications to secure communication in theory. First, we construct the complex MVDPD oscillator and analysis its chaotic behavior. Moreover, an observer design method is applied to achieve PS of two identical MVDPD chaotic oscillators with complex offset terms, which are synchronized to the desired scale factor. The unpredictability of the scaling factor could further enhance the security of the communication. Finally, numerical simulations are given to demonstrate the effectiveness and feasibility of the proposed synchronization approach and also verify the success application to the proposed scheme’s in the secure communication.

PROJECTIVE SYNCHRONIZATION OF TWO DIFFERENT DIMENSIONAL NONLINEAR SYSTEMS

2013 ◽  
Vol 27 (21) ◽  
pp. 1350113 ◽  
Author(s):  
FUZHONG NIAN ◽  
XINGYUAN WANG
Keyword(s):  
Nonlinear Systems ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Drive System ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Response System ◽  
Opposite Situation ◽  
The One ◽  
Hyperchaotic Systems

Projective synchronization between two nonlinear systems with different dimension was investigated. The controllers were designed when the dimension of drive system greater than the one of response system. The opposite situation also was discussed. In addition, we found an approach to control the chaotic (hyperchaotic) system to exhibit the behaviors of hyperchaotic (chaotic) system. The numerical simulations were implemented on different chaotic (hyperchaotic) systems, and the results indicate that our methods are effective.

Well-Conditioned Observer Design for Observer-Based Monitoring Systems

1995 ◽  
Vol 117 (4) ◽  
pp. 592-599 ◽  
Author(s):  
Kunsoo Huh ◽  
J. L. Stein
Keyword(s):  
Upper Bound ◽  
Performance Index ◽  
Block Design ◽  
Design Procedure ◽  
Poor Performance ◽  
Design Strategy ◽  
Observer Design ◽  
Pole Placement ◽  
Monitoring Systems ◽  
Remote Sensors

Observer-based monitoring systems for machine diagnostics and control are receiving increased attention. These observer techniques can estimate process and machine variables from inexpensive, easy to install remote sensors based on state-space models of the machine structure between the machine variables of interest and the location of the remote sensors. Unfortunately, these observers can be ill-conditioned and this leads to poor performance. The authors have previously shown that observer performance can be represented by a single performance index, the condition number of the eigensystem of the state observer matrix and that there exists an upper bound for the index in non-normal matrices and the bound can be determined by the structure and eigenvalues of the observer matrix. In this paper, a design methodology for synthesizing well-conditioned observers is proposed based on the upper bound of the performance index. The methodology is based on the fact that a small upper bound guarantees small values of the performance index. A well-conditioned matrix form is defined and a block-by block design strategy to produce a well-conditioned observer matrix is presented. A complete design procedure for well-conditioned deterministic state observers is given for the single-output case. The design strategy is illustrated with an example that shows that the proposed well-conditioned observer performs much better than an observer designed with traditional pole placement techniques.

scholarly journals Projective Synchronization of a 3D Chaotic System with Quadratic and Quartic Nonlinearities

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Babatunde Idowu ◽  
Kehinde Oyeleke ◽  
Cornelius Ogabi ◽  
Olasunkanmi Olusola
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Adaptive Synchronization ◽  
Dimensional System

Introduction: In this work, the projective synchronization of two identical three dimensional chaotic system with quadratic and quartic non linearities was considered as well as the equilibrium and stability analysis of the system. The projective synchronization with same and different scaling factor was carried out for this category of system to show its feasibility in order to establish that no matter the type and number of nonlinearities, projective synchronization can be achieved. Numerical simulations was done to verify the above. In all kinds of chaos synchronization, projective synchronization (PS), characterized by a scaling factor that two systems synchronize proportionally, is one of the most interesting problems. It was first reported by Mainieri et al [1] , where it was stated that the two identical systems (master and slave) could be synchronized up to a scaling factor, . They further stated that the scaling factor was dependent on the chaotic evolution and initial conditions so that the ultimate state of projective synchronization was unpredictable. Aims: Is to achieve projective synchronization of two identical three Dimensional chaotic system with quadratic and quartic nonlinearities synchronizing to a scaling factor and also present the equilibrium and stability analysis of the system. This is to establish that projective synchronization can be achieved for varied systems with varied nonlinearities. Materials and Methods: We employed the adaptive synchronization technique to achieve projective synchronization of the system (master and slave) with different scaling factors, and the fourth order RungeKutta algorithm is used for numerical solutions. Results: In this work, the projective synchronization of two identical three dimensional systems with quadratic and quartic nonlinearities was achieved with the same and different scaling factor, . The equilibrium and stability analysis of the system was also presented. Numerical simulations was done to verify the above. Conclusion: The investigated projective synchronization behaviour of two identical three-dimensional system with two nonlinearities (quadratic and quartic) was achieved for cases where the scaling factor is the same and when different. This shows that projective synchronization can be achieved for systems with varying nonlinearities even when the scaling factor is different and this suggests its use in communication using chaotic wave forms as carriers, perhaps with a view to securing communication.

scholarly journals Compound Generalized Function Projective Synchronization for Fractional-Order Chaotic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Chunde Yang ◽  
Hao Cai ◽  
Ping Zhou
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Drive System ◽  
Projective Synchronization ◽  
Order System ◽  
Generalized Function ◽  
Function Projective Synchronization ◽  
The Stability ◽  
Generalized Function Projective Synchronization

A modified function projective synchronization for fractional-order chaotic system, called compound generalized function projective synchronization (CGFPS), is proposed theoretically in this paper. There are one scaling-drive system, more than one base-drive system, and one response system in the scheme of CGFPS, and the scaling function matrices come from multidrive systems. The proposed CGFPS technique is based on the stability theory of fractional-order system. Moreover, we achieve the CGFPS between three-driver chaotic systems, that is, the fractional-order Arneodo chaotic system, the fractional-order Chen chaotic system, and the fractional-order Lu chaotic system, and one response chaotic system, that is, the fractional-order Lorenz chaotic system. Numerical experiments are demonstrated to verify the effectiveness of the CGFPS scheme.

ADAPTIVE FULL STATE HYBRID PROJECTIVE SYNCHRONIZATION IN THE UNIFIED CHAOTIC SYSTEM

2009 ◽  
Vol 23 (15) ◽  
pp. 1913-1921 ◽  
Author(s):  
XINGYUAN WANG ◽  
JUNMEI SONG
Keyword(s):  
Dynamical System ◽  
Chaotic System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Response System ◽  
Unified Chaotic System ◽  
Full State ◽  
Hybrid Projective Synchronization

This paper studies the adaptive full state hybrid projective synchronization method. Based on the Lyapunov stability theory, an adaptive controller is designed. It is proved theoretically that the controller can make the states of the dynamical system and the response system with known or unknown parameters asymptotically full state hybrid projective synchronized. A unified chaotic system is used as an example and numerical simulations show the effectiveness of the scheme.

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