Synchronization of three dimensional chaotic systems via a single state feedback

2011 ◽  
Vol 16 (7) ◽  
pp. 2880-2886 ◽  
Author(s):  
Wenguang Yu
Keyword(s):  
State Feedback ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
Single State

Synchronization of a Class of Chaotic and Hyperchaotic Systems via a Simple Universal Control Method

2012 ◽  
Vol 184-185 ◽  
pp. 798-801
Author(s):  
Zhi Liu ◽  
Ming Ju Hao
Keyword(s):  
Chaos Synchronization ◽  
State Feedback ◽  
Chaotic Systems ◽  
Control Method ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Universal Method ◽  
Error System ◽  
Single State ◽  
Hyperchaotic Systems

This paper investigates the synchronization of chaotic and hyperchaotic systems, and proposes a simple and universal method for chaos synchronization through investigating the dynamical behavior of the chaotic error system. In comparison with previous methods, the present controllers are simpler than the existing results. Especially, for some class of three dimensional chaotic systems, the obtained controllers in this paper contain single state feedback. Numerical simulations verify the effectiveness and correctness of the proposed method.

Single state feedback stabilization of unified chaotic systems and circuit implementation

Open Physics ◽  
2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Chun-Guo Jing ◽  
Ping He ◽  
Tao Fan ◽  
Yangmin Li ◽  
Changzhong Chen ◽  
...  
Keyword(s):  
Chaotic System ◽  
State Feedback ◽  
Chaotic Systems ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Uncertain Parameter ◽  
Circuit Implementation ◽  
Unified Chaotic System ◽  
Unified Chaotic Systems ◽  
Single State

AbstractThis paper focuses on the single state feedback stabilization problem of unified chaotic system and circuit implementation. Some stabilization conditions will be derived via the single state feedback control scheme. The robust performance of controlled unified chaotic systems with uncertain parameter will be investigated based on maximum and minimum analysis of uncertain parameter, the robust controller which only requires information of a state of the system is proposed and the controller is linear. Both the unified chaotic system and the designed controller are synthesized and implemented by an analog electronic circuit which is simpler because only three variable resistors are required to be adjusted. The numerical simulation and control in MATLAB/Simulink is then provided to show the effectiveness and feasibility of the proposed method which is robust against some uncertainties. The results presented in this paper improve and generalize the corresponding results of recent works.

A New Category of Three-Dimensional Chaotic Flows with Identical Eigenvalues

2020 ◽  
Vol 30 (02) ◽  
pp. 2050026 ◽  
Author(s):  
Zahra Faghani ◽  
Fahimeh Nazarimehr ◽  
Sajad Jafari ◽  
Julien C. Sprott
Keyword(s):  
Chaotic Systems ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Special Property ◽  
Computer Search ◽  
Chaotic Flows ◽  
Stable Equilibria ◽  
Dynamical Properties ◽  
Simple Systems ◽  
First Time

In this paper, some new three-dimensional chaotic systems are proposed. The special property of these autonomous systems is their identical eigenvalues. The systems are designed based on the general form of quadratic jerk systems with 10 terms, and some systems with stable equilibria. Using a systematic computer search, 12 simple chaotic systems with identical eigenvalues were found. We believe that systems with identical eigenvalues are described here for the first time. These simple systems are listed in this paper, and their dynamical properties are investigated.

scholarly journals A NONLINEAR STATE FEEDBACK APPROACH TO THE CONTROL AND SYNCHRONIZATION OF CONTINUOUS-TIME CHAOTIC SYSTEMS

1999 ◽  
Vol 48 (9) ◽  
pp. 1618
Author(s):  
GAO JIN-FENG ◽  
LUO XIAN-JUE ◽  
MA XI-KUI ◽  
PAN XIU-QIN ◽  
WANG JUN-KUN
Keyword(s):  
Continuous Time ◽  
State Feedback ◽  
Chaotic Systems ◽  
Control And Synchronization ◽  
Nonlinear State

scholarly journals Design of a Nonhomogeneous Nonlinear Synchronizer and Its Implementation in Reconfigurable Hardware

2020 ◽  
Vol 25 (3) ◽  
pp. 51
Author(s):  
Jesus R. Pulido-Luna ◽  
Jorge A. López-Rentería ◽  
Nohe R. Cazarez-Castro
Keyword(s):  
Asymptotic Stability ◽  
Test Performance ◽  
State Feedback ◽  
Chaotic Systems ◽  
Reconfigurable Hardware ◽  
Lyapunov Theory ◽  
Control Law ◽  
Heterogeneous Dynamics ◽  
Two Systems ◽  
Error State

In this work, a generalization of a synchronization methodology applied to a pair of chaotic systems with heterogeneous dynamics is given. The proposed control law is designed using the error state feedback and Lyapunov theory to guarantee asymptotic stability. The control law is used to synchronize two systems with different number of scrolls in their dynamics and defined in a different number of pieces. The proposed control law is implemented in an FPGA in order to test performance of the synchronization schemes.

scholarly journals The Design and Its Application in Secure Communication and Image Encryption of a New Lorenz-Like System with Varying Parameter

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Lilian Huang ◽  
Donghai Shi ◽  
Jie Gao
Keyword(s):  
Numerical Simulation ◽  
Secure Communication ◽  
State Feedback ◽  
Complex Dynamic ◽  
State Variable ◽  
Encryption And Decryption ◽  
Single State ◽  
Chaotic Parameter ◽  
Synchronization Scheme ◽  
New System

A new Lorenz-like chaotic system with varying parameter is proposed by adding a state feedback function. The structure of the new designed system is simple and has more complex dynamic behaviors. The chaos behavior of the new system is studied by theoretical analysis and numerical simulation. And the bifurcation diagram shows a chaos-cycle-chaos evolution when the new parameter changes. Then a new synchronization scheme by a single state variable drive is given based on the new system and a chaotic parameter modulation digital secure communication system is also constructed. The results of simulation demonstrate that the new proposed system could be well applied in secure communication. Otherwise, based on the new system, the encryption and decryption of image could be achieved also.

ROTATING SYNCHRONIZATION IN THREE-DIMENSIONAL CHAOTIC SYSTEMS

2012 ◽  
Vol 26 (20) ◽  
pp. 1250120 ◽  
Author(s):  
FUZHONG NIAN ◽  
XINGYUAN WANG
Keyword(s):  
Phase Space ◽  
Chaotic Systems ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Phase Space Reconstruction ◽  
Projective Synchronization ◽  
Reconstruction Method ◽  
Self Similarity ◽  
Application Fields ◽  
Three Dimensional Space

Projective synchronization investigates the synchronization of systems evolve in same orientation, however, in practice, the situation of same orientation is only minority, and the majority is different orientation. This paper investigates the latter, proposes the concept of rotating synchronization, and verifies its necessity and feasibility via theoretical analysis and numerical simulations. Three conclusions were elicited: first, in three-dimensional space, two arbitrary nonlinear chaotic systems who evolve in different orientation can realize synchronization at end; second, projective synchronization is a special case of rotating synchronization, so, the application fields of rotating synchronization is more broadly than that of the former; third, the overall evolving information can be reflected by single state variable's evolving, it has self-similarity, this is the same as the basic idea of phase space reconstruction method, it indicates that we got the same result from different approach, so, our method and the phase space reconstruction method are verified each other.

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