scholarly journals Predefined-time vector-polynomial-based synchronization among a group of chaotic systems and its application in secure information transmission

2021 ◽  
Vol 6 (10) ◽  
pp. 11005-11028
Author(s):  
Qiaoping Li ◽  
◽  
Sanyang Liu ◽  
Keyword(s):  
Information Transmission ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Chaotic Synchronization ◽  
Synchronization Control ◽  
Control Technology ◽  
Theoretical Derivation ◽  
Secure Information ◽  
Synchronization Scheme ◽  
Vector Polynomial

<abstract><p>This article aims to improve the security and timeliness of chaotic synchronization scheme in chaotic secure information transmission. Firstly, a novel nonlinear synchronization scheme among multiple chaotic systems is defined based on vector polynomial to improve the complexity of the carrier signal, and then to enhance the attack resistance of the communication scheme. Secondly, a more flexible and accurate synchronization control technology is proposed so that the above vector-polynomial-based chaotic synchronization can be realized within a time that is predefined as a tunable control parameter. Subsequently, the theoretical derivation is carried out to prove the synchronization time in the above-mentioned synchronization control scheme can be set independently without being affected by the initial conditions or other control parameters. Finally, several simulation experiments on secure information transmission are presented to verify the efficiency and superiority of the designed chaotic synchronization scheme and synchronization control technology.</p></abstract>

The Synchronization of Super-Chen Chaotic Scheme with a Sort of Oscillating Parameters

2011 ◽  
Vol 282-283 ◽  
pp. 612-615
Author(s):  
Ying Kui Li
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Chaotic Synchronization ◽  
Control Signal ◽  
Synchronization Control ◽  
Two Systems ◽  
Control And Synchronization ◽  
Synchronization Scheme

Most properties of Super Chen’s chaotic system satisfy with the requirements of secure communication and cryptography. Implusive stabilzation for control and synchronization of Super Chen’s chaotic systems can be applied in secure communication. Super Chen’s Chaotic synchronization control can be the kernel technology in chaos-based secure commu-nication. In this paper we propose a hybrid Super Chen chaotic synchronization scheme control which contains both continuous chaotic system with a sort of oscillating parameters and discrete chaotic system. If oscillating parameters approach to 0, we proved that two systems can get synchronized without control signal transmitting.

The Model of Liu Chaotic Synchronization with Oscillating Parameters under the Impulsive Control

2011 ◽  
Vol 480-481 ◽  
pp. 1378-1382
Author(s):  
Yan Hui Chen
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Chaotic Synchronization ◽  
Control Signal ◽  
Synchronization Control ◽  
Security Risks ◽  
Control Scheme

The control of chaotic synchronization is the kernel technology in chaos-based secure communication. Those control methods have to transmitting control signal which increase the security risks of the communication system. Attacker can reconstruct the chaotic system or estimate parameters by using the information of the chaotic system. In this paper we propose a hybrid Liu chaotic synchronization control scheme which contains both continuous chaotic system with oscillating parameters approach to 0 and discrete chaotic system. By theory of impulsive differential equations, we proved a theorem that two continuous Liu chaotic systems can get synchronized without control signal transmitting which has reduced the risk of the security.

scholarly journals Compound-combination synchronization of chaos in identical and different orders chaotic systems

2015 ◽  
Vol 25 (4) ◽  
pp. 463-490 ◽  
Author(s):  
K. S. Ojo ◽  
A. N. Njah ◽  
O. I. Olusola
Keyword(s):  
Chaotic Systems ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Backstepping Technique ◽  
Third Order ◽  
Combination Synchronization ◽  
Response Systems ◽  
Drive Systems ◽  
Synchronization Scheme ◽  
Insight Into

Abstract This paper proposes a new synchronization scheme called compound-combination synchronization. The scheme is investigated using six chaotic Josephson junctions evolving from different initial conditions based on the drive-response configuration via the active backstepping technique. The technique is applied to achieve compound-combination synchronization of: (i) six identical third order resistive-capacitive-inductive-shunted Josepshon junctions (RCLSJJs) (with three as drive and three as response systems); (ii) three third order RCLSJJs (as drive systems) and three second order resistive-capacitive-shunted Josepshon junctions (RCSJJs (as response systems). In each case, sufficient conditions for global asymptotic stability for compound-combination synchronization to any desired scaling factors are achieved. Numerical simulations are employed to verify the feasibility and effectiveness of the compound-combination synchronization scheme. The result shows that this scheme could be used to vary the junction signal to any desired level and also give a better insight into synchronization in biological systems wherein different organs of different dynamical structures and orders are involved. The scheme could also provide high security in information transmission due to the complexity of its dynamical formulation.

GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS

2011 ◽  
Vol 25 (09) ◽  
pp. 1283-1292 ◽  
Author(s):  
MING-JUN WANG ◽  
XING-YUAN WANG
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Chaotic Synchronization ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
Different Dimensions ◽  
The Stability ◽  
Synchronization Scheme

In the paper, generalized chaotic synchronization of a class of fractional order systems is studied. Based on the stability theory of linear fractional order systems, a generalized synchronization scheme is presented, and theoretical analysis is provided to verify its feasibility. The proposed method can realize generalized synchronization not only of fractional order systems with same dimension, but also of systems with different dimensions. Besides, the function relation of generalized synchronization can be linear or nonlinear. Numerical simulations show the effectiveness of the scheme.

scholarly journals Synchronization of cyclic coupled hyperchaotic systems and its circuit implementation

2019 ◽  
pp. 267-276
Author(s):  
K.S. Ojo ◽  
A.O. Adelakun ◽  
A. I. Egunjobi ◽  
E. I. Udoh
Keyword(s):  
Information Transmission ◽  
Chaotic Systems ◽  
Analog Circuit ◽  
Biological Information ◽  
Circuit Implementation ◽  
Transmission Networks ◽  
Synchronization Time ◽  
Potential Applications ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

Most of the available research works on cyclic coupling of chaotic systems focussed on either analytical and numerical results or numerical and experimental results. This research paper, investigates synchronization of two cyclic coupled hyperchaotic systems using analytical, numerical and experimental techniques. Based on Routh-Hurwitz criterion, analytical condition for stable synchronization of the hyperchaotic systems are derived. The results obtained from MultiSIM and analog circuit confirm the effectiveness and feasibility of the analytical results. It is worthy of note that the cyclic coupling synchronization scheme gives several synchronization options, save synchronization time and cost. Moreover, cyclic coupling synchronization scheme has potential applications in biological information transmission networks.

A Novel Adaptive Active Control Projective Synchronization of Chaotic Systems

2018 ◽  
Vol 13 (5) ◽  
Author(s):  
Boan Quan ◽  
Chunhua Wang ◽  
Jingru Sun ◽  
Yilin Zhao
Keyword(s):  
Active Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Chaotic Synchronization ◽  
Diagonal Matrix ◽  
Projective Synchronization ◽  
Adaptive Synchronization ◽  
Control Schemes ◽  
Error System ◽  
Synchronization Scheme

This paper investigates adaptive active control projective synchronization scheme. A general synchronization controller and parameter update laws are proposed to stabilize the error system for the identical structural chaotic systems. It is the first time that the active synchronization, the projective synchronization, and the adaptive synchronization are combined to achieve the synchronization of chaotic systems, which extend the control capability of achieving chaotic synchronization. By using a constant diagonal matrix, the active control is developed. Especially, when designing the controller, we just need to ensure that the diagonal elements of the diagonal matrix are less than or equal 0. So, the synchronization of chaotic systems can be realized more easily. Furthermore, by proposing an active controller, in combination with several different control schemes, we lower the complexity of the design process of the controller. More importantly, the larger the absolute value of product of the diagonal elements of diagonal matrix is, the smoother the curve of chaotic synchronization is and the shorter the time of chaotic synchronization is. In our paper, we take Lorenz system as an example to verify the effectiveness of the proposed synchronization scheme. Theoretical analysis and numerical simulations demonstrate the feasibility of this control method.

Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter

Open Physics ◽  
2012 ◽  
Vol 10 (5) ◽  
Author(s):  
Hadi Delavari ◽  
Danial Senejohnny ◽  
Dumitru Baleanu
Keyword(s):  
Lyapunov Function ◽  
Fractional Order ◽  
Canonical Form ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Chaotic Synchronization ◽  
Mode Theory ◽  
Synchronization Scheme

AbstractIn this paper, we propose an observer-based fractional order chaotic synchronization scheme. Our method concerns fractional order chaotic systems in Brunovsky canonical form. Using sliding mode theory, we achieve synchronization of fractional order response with fractional order drive system using a classical Lyapunov function, and also by fractional order differentiation and integration, i.e. differintegration formulas, state synchronization proved to be established in a finite time. To demonstrate the efficiency of the proposed scheme, fractional order version of a well-known chaotic system; Arnodo-Coullet system is considered as illustrative examples.

scholarly journals Synchronization of Two Rank-One Chaotic Systems without and with Delay via Linear Delayed Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hui Fang
Keyword(s):  
Feedback Control ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Chaotic Synchronization ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Rank One ◽  
Feedback Control Method ◽  
Synchronization Scheme

This paper illustrates the presence of chaos in rank-one chaotic systems with delay via a binary test (called 0-1 test) for chaos. Chaotic synchronization between two rank-one chaotic systems without and with delay is achieved by means of Lyapunov functional and linear delayed feedback control method. Numerical simulations are implemented to verify the effectiveness of the proposed chaos synchronization scheme.

scholarly journals Spontaneous Synchronization in Two Mutually Coupled Memristor-Based Chua’s Circuits: Numerical Investigations

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Eleonora Bilotta ◽  
Francesco Chiaravalloti ◽  
Pietro Pantano
Keyword(s):  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Synchronization Control ◽  
Time Varying ◽  
Cubic Nonlinearity ◽  
Numerical Investigations ◽  
Self Organized ◽  
Coupling Resistance ◽  
Coupled Circuits

Chaotic dynamics of numerous memristor-based circuits is widely reported in literature. Recently, some works have appeared which study the problem of synchronization control of these systems in a master-slave configuration. In the present paper, the spontaneous dynamic behavior of two chaotic memristor-based Chua’s circuits, mutually interacting through a coupling resistance, was studied via computer simulations in order to study possible self-organized synchronization phenomena. The used memristor is a flux controlled memristor with a cubic nonlinearity, and it can be regarded as a time-varying memductance. The memristor, in effect, retains memory of its past dynamic and any difference in the initial conditions of the two circuits results in different values of the corresponding memductances. In this sense, due to the memory effect of the memristor, even if coupled circuits have the same parameters they do not constitute two completely identical chaotic oscillators. As is known, for nonidentical chaotic systems, in addition to complete synchronizations (CS) other weaker forms of synchronization which provide correlations between the signals of the two systems can also occur. Depending on initial conditions and coupling strength, both chaotic and nonchaotic synchronization are observed for the system considered in this work.

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