Synchronization in coupled fractional order Chen-system and its application in secure communication

2009 ◽  
Author(s):  
Yan-Song Deng ◽  
Kai-Yu Qin ◽  
Shi-Quan Shao
Keyword(s):  
Fractional Order ◽  
Secure Communication ◽  
Chen System

CHAOS GENERATED FROM THE FRACTIONAL-ORDER COMPLEX CHEN SYSTEM AND ITS APPLICATION TO DIGITAL SECURE COMMUNICATION

2013 ◽  
Vol 24 (04) ◽  
pp. 1350025 ◽  
Author(s):  
CHAO LUO ◽  
XINGYUAN WANG
Keyword(s):  
Fractional Order ◽  
Secure Communication ◽  
High Capacity ◽  
Projective Synchronization ◽  
Largest Lyapunov Exponent ◽  
Order Complex ◽  
State Variables ◽  
Chen System ◽  
Time Dynamic ◽  
Irregular Pattern

In this paper, a novel dynamic system, the fractional-order complex Chen system, is presented for the first time. Dynamic behaviors of system are studied analytically and numerically. Different routes to chaos are shown, and diverse kinds of motions are identified and exhibited by means of bifurcation diagram, portrait phase and the largest Lyapunov exponent. Secondly, an application to digital secure communication based on the novel system is proposed, in which security is enhanced by continually switching different orders of derivative in an irregular pattern. Furthermore, making full use of the advantage of high-capacity transmission of complex system, the improved digital secure communication scheme is achieved based on hybrid synchronization in coupled fractional-order complex Chen system, that means anti-synchronization in real part of state variables and projective synchronization in imaginary part, respectively. The corresponding numerical simulations demonstrate the effectiveness and feasibility of the proposed schemes.

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.

Comparison of Times of Synchronization of Chaotic Burke-Shaw Attractor with Active Control and Integer and Optimum Fractional-Order Pecaro Carroll Method

2021 ◽  
Author(s):  
Ali Durdu ◽  
Yılmaz Uyaroğlu
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Attractor ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Initial Conditions ◽  
Data Communication ◽  
Experimental Results ◽  
Active Control Method

Abstract Many studies have been introduced in the literature showing that two identical chaotic systems can be synchronized with different initial conditions. Secure data communication applications have also been made using synchronization methods. In the study, synchronization times of two popular synchronization methods are compared, which is an important issue for communication. Among the synchronization methods, active control, integer, and fractional-order Pecaro Carroll (P-C) method was used to synchronize the Burke-Shaw chaotic attractor. The experimental results showed that the P-C method with optimum fractional-order is synchronized in 2.35 times shorter time than the active control method. This shows that the P-C method using fractional-order creates less delay in synchronization and is more convenient to use in secure communication applications.

scholarly journals Study on Chaotic Fault Tolerant Synchronization Control Based on Adaptive Observer

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Dongming Chen ◽  
Xinyu Huang ◽  
Tao Ren
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Fault Tolerant ◽  
Sufficient Conditions ◽  
Adaptive Observer ◽  
Synchronization Control ◽  
Slave System ◽  
Chen System ◽  
Master System ◽  
Abrupt Faults

Aiming at the abrupt faults of the chaotic system, an adaptive observer is proposed to trace the states of the master system. The sufficient conditions for synchronization of such chaotic systems are also derived. Then the feasibility and effectiveness of the proposed method are illustrated via numerical simulations of chaotic Chen system. Finally, the proposed synchronization schemes are applied to secure communication system successfully. The experimental results demonstrate that the employed observer can manage real-time fault diagnosis and parameter identification as well as states tracing of the master system, and so the synchronization of master system and slave system is achieved.

scholarly journals Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

scholarly journals Chaos in the fractional-order conjugate Chen system and its circuit emulation

2009 ◽  
Vol 58 (5) ◽  
pp. 2957
Author(s):  
Zhang Ruo-Xun ◽  
Yang Shi-Ping
Keyword(s):  
Fractional Order ◽  
Chen System
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