Chaotic Synchronization of Nonlinear-Coupled Fractional-order Liu System and Secure Communication

In this paper, chaos in complex-order Chua’s system and its chaotic synchronization for secure communication are studied based on the fractional derivative investigated. Chaos in complex-order Chua’s system is illustrated by presenting its waveform graphs, states diagrams and bifurcation graphs. The dynamic behaviors in the complex-order Chua’s system and time-delayed Chua’s system are compared. In addition, the largest Lyapunov exponents of normal and time-delayed Chua’s systems are calculated and verified by numerical simulations. The experiment indicates that the chaos in such Chua’s system can achieve two channel communications.

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

Mathematical Problems in Engineering ◽

10.1155/2015/941654 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9 ◽

Cited By ~ 4

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.

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

10.21203/rs.3.rs-263593/v1 ◽

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.

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