scholarly journals Analytical and Numerical Study of the Projective Synchronization of the Chaotic Complex Nonlinear Systems with Uncertain Parameters and Its Applications in Secure Communication

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Kholod M. Abualnaja ◽  
Emad E. Mahmoud
Keyword(s):  
Applied Sciences ◽  
Nonlinear Systems ◽  
Secure Communication ◽  
Numerical Study ◽  
Projective Synchronization ◽  
Control Technique ◽  
Uncertain Parameters ◽  
Complex Nonlinear Systems ◽  
Synchronization Scheme ◽  
Theoretical Results

The main aim of this research is to find an analytical and numerical study to investigate the projective synchronization of two identical or nonidentical chaotic complex nonlinear systems with uncertain parameters. The secure communication between these systems is achieved based on this study. Based on the adaptive control technique and the Lyapunov function a scheme is designed to achieve projective synchronization of chaotic attractors of these systems. The projective synchronization of two identical complex Chen systems and two different chaotic complex Lü and Lorenz systems is taken as two examples to verify the feasibility of the presented scheme. These chaotic complex systems appear in several applications in physics, engineering, and other applied sciences. Numerical simulations are calculated to demonstrate the effectiveness of the proposed synchronization scheme and verify the theoretical results. The above results will provide theoretical foundation for the secure communication applications based on the proposed scheme.

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

Generalized Hybrid Dislocated Function Projective Synchronization of Chaotic Systems with Time Delay

2014 ◽  
Vol 574 ◽  
pp. 672-678 ◽  
Author(s):  
Rui Li ◽  
Guang Jun Zhang ◽  
Tao Zhu ◽  
Xu Jing Wang ◽  
Jun Dong
Keyword(s):  
Time Delay ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Feedback Gain ◽  
Uncertain Parameters ◽  
Function Projective Synchronization ◽  
Feedback Control Method

In order to improve the security of secure communication, a novel generalized hybrid dislocated function projective synchronization (GHDFPS) was proposed and GHDFPS of time delay chaotic systems with uncertain parameters were researched in this paper. Due to time delay, the chaotic system can produce multiple positive Lyapunov exponential; this characteristic can enhance security in secure communications noticeably. Based on Lyapunove stability theory and modified hybrid feedback control method, the modified hybrid feedback controller and the parameter updating laws were designed for the GHDFPS between the two time delay chaotic systems with uncertain parameters. The feedback gain can be adjusted automatically according to the synchronization error values. Under the controller, generalized hybrid dislocated function projective synchronization of the two chaotic systems is achieved, and the uncertain parameters of response systems are identified. The chaotic item is added in the function scale factor. The chaotic item in the function scaling factor makes function scaling factor more complex and unpredictable. So this can enhance the features of indeterminism in secure communication. The time delay feedback Lorenz system as an example; by numerical simulations the effectiveness of the proposed method is demonstrated.

scholarly journals Combination-Combination Projective Synchronization of Multiple Chaotic Systems Using Sliding Mode Control

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Junwei Sun ◽  
Nan Li ◽  
Jie Fang
Keyword(s):  
Sliding Mode Control ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Mode Control ◽  
Adaptive Laws ◽  
Different Chaotic Systems ◽  
Synchronization Scheme ◽  
Multiple Chaotic Systems

Based on projective synchronization and combination synchronization model, a type of combination-combination projective synchronization is realized via nonsingular sliding mode control technique for multiple different chaotic systems. Concretely, on the basic of the adaptive laws and stability theory, the corresponding sliding mode control surfaces and controllers are designed to achieve the combination-combination projective synchronization between the combination of two chaotic systems as drive system and the combination of multiple chaotic systems as response system with disturbances. Some criteria and corollaries are derived for combination-combination projective synchronization of the multiple different chaotic systems. Finally, the numerical simulation results are presented to demonstrate the effectiveness and correctness of the synchronization scheme.

scholarly journals Projective Synchronization ofN-Dimensional Chaotic Fractional-Order Systems via Linear State Error Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Baogui Xin ◽  
Tong Chen
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Projective Synchronization ◽  
Control Technique ◽  
Linear Feedback ◽  
Fractional Order Systems ◽  
Financial Systems ◽  
Linear State ◽  
Synchronization Scheme ◽  
State Error

Based on linear feedback control technique, a projective synchronization scheme ofN-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stability theory of linear fractional order systems, a suitable controller for achieving synchronization is designed. The given scheme is applied to achieve projective synchronization of chaotic fractional-order financial systems. Numerical simulations are given to verify the effectiveness of the proposed projective synchronization scheme.

Active Control for Multi-Switching Combination Synchronization of Non-Identical Chaotic Systems

2018 ◽  
pp. 129-162 ◽  
Author(s):  
Shikha Singh ◽  
Ahmad Taher Azar ◽  
Muzaffar Ahmad Bhat ◽  
Sundarapandian Vaidyanathan ◽  
Adel Ouannas
Keyword(s):  
Information Security ◽  
Numerical Simulations ◽  
Active Control ◽  
Chaotic Systems ◽  
Control Technique ◽  
Slave System ◽  
Combination Synchronization ◽  
Wide Range ◽  
Synchronization Scheme ◽  
Theoretical Results

This chapter investigates the multi-switching combination synchronization of three non-identical chaotic systems via active control technique. In recent years, some advances have been made with the idea of multi-switching combination synchronization. The different states of the master systems are synchronized with the desired state of the slave system in multi-switching combination synchronization scheme. The relevance of such kinds of synchronization studies to information security is evident in the wide range of possible synchronization directions that exist due to multi-switching synchronization. Numerical simulations justify the validity of the theoretical results discussed.

Hybrid Projective Synchronization of Fractional-Order Chaotic Complex Nonlinear Systems With Time Delays

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
G. Velmurugan ◽  
R. Rakkiyappan
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
Time Delays ◽  
Lorenz System ◽  
Projective Synchronization ◽  
Nonlinear Controller ◽  
Scaling Factors ◽  
Hybrid Projective Synchronization ◽  
Complex Nonlinear Systems ◽  
Complex Lorenz System

Time delays are frequently appearing in many real-life phenomena and the presence of time delays in chaotic systems enriches its complexities. The analysis of fractional-order chaotic real nonlinear systems with time delays has a plenty of interesting results but the research on fractional-order chaotic complex nonlinear systems with time delays is in the primary stage. This paper studies the problem of hybrid projective synchronization (HPS) of fractional-order chaotic complex nonlinear systems with time delays. HPS is one of the extensions of projective synchronization, in which different state vectors can be synchronized up to different scaling factors. Based on Laplace transformation and the stability theory of linear fractional-order systems, a suitable nonlinear controller is designed to achieve synchronization between the master and slave fractional-order chaotic complex nonlinear systems with time delays in the sense of HPS with different scaling factors. Finally, the HPS between fractional-order delayed complex Lorenz system and fractional-order delayed complex Chen system and that of fractional-order delayed complex Lorenz system and fractional-order delayed complex Lu system are taken into account to demonstrate the effectiveness and feasibility of the proposed HPS techniques in the numerical example section.

scholarly journals Hybrid Projective Synchronization of 4-D Hyperchaotic Systems via Adaptive Control

2020 ◽  
Vol 12 (2) ◽  
pp. 201-208
Author(s):  
A. Khan ◽  
H. Chaudhary
Keyword(s):  
Adaptive Control ◽  
Asymptotic Stability ◽  
Secure Communication ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Control Technique ◽  
Complete Agreement ◽  
Suggested Technique ◽  
Hybrid Projective Synchronization ◽  
Hyperchaotic Systems

This paper designs a procedure for investigating the hybrid projective synchronization (HPS) scheme between two identical 4-D hyperchaotic systems. Based on Lyapunov stability theory (LST), an adaptive control technique (ACT) has been designed to achieve the desired HPS scheme. The suggested technique determines globally the asymptotic stability and identification of parameters simultaneously using HPS scheme. It is noted that complete , hybrid and anti-synchronization turns into particular cases of HPS scheme. Numerical simulations are presented to validate the effectivity and feasibleness of the considered technique by using MATLAB. Remarkably, the theoretical and computational outcomes are in complete agreement. Also, the considered HPS scheme is very efficient as it has numerous applications in encryption and secure communication.

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