scholarly journals Synchronization of fractional-order unified chaotic system via linear control

2010 ◽  
Vol 59 (3) ◽  
pp. 1549
Author(s):  
Zhang Ruo-Xun ◽  
Yang Shi-Ping ◽  
Liu Yong-Li
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Linear Control ◽  
Unified Chaotic System

scholarly journals Chaos Synchronization between Fractional-Order Unified Chaotic System and Rossler Chaotic System

2012 ◽  
Vol 562-564 ◽  
pp. 2088-2091
Author(s):  
Xian Yong Wu ◽  
Yi Long Cheng ◽  
Kai Liu ◽  
Xin Liang Yu ◽  
Xian Qian Wu
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Dynamics ◽  
Chaotic Attractors ◽  
System Parameters ◽  
Unified Chaotic System ◽  
Simulation Results ◽  
Drive Systems ◽  
Asymptotic Synchronization

The chaotic dynamics of the unified chaotic system and the Rossler system with different fractional-order are studied in this paper. The research shows that the chaotic attractors can be found in the two systems while the orders of the systems are less than three. Asymptotic synchronization of response and drive systems is realized by active control through designing proper controller when system parameters are known. Theoretical analysis and simulation results demonstrate the effective of this method.

Circuit realization of the fractional-order unified chaotic system

2008 ◽  
Vol 17 (5) ◽  
pp. 1664-1669 ◽  
Author(s):  
Chen Xiang-Rong ◽  
Liu Chong-Xin ◽  
Wang Fa-Qiang
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Circuit Realization ◽  
Unified Chaotic System

scholarly journals Dual Penta-Compound Combination Anti-Synchronization with Analysis and Application to a Novel Fractional Chaotic System

2021 ◽  
Vol 5 (4) ◽  
pp. 264
Author(s):  
Lone Seth Jahanzaib ◽  
Pushali Trikha ◽  
Rajaa T. Matoog ◽  
Shabbir Muhammad ◽  
Ahmed Al-Ghamdi ◽  
...  
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Linear Control ◽  
Stagnation Points ◽  
Fractional Chaotic System ◽  
The Impact ◽  
Mode Technique ◽  
Sliding Mode Technique

This paper studies a fractional-order chaotic system with sine non-linearities and highlights its dynamics using the Lyapunov spectrum, bifurcation analysis, stagnation points, the solution of the system, the impact of the fractional order on the system, etc. The system considering uncertainties and disturbances was synchronized using dual penta-compound combination anti-synchronization among four master systems and twenty slave systems by non-linear control and the adaptive sliding mode technique. The estimates of the disturbances and uncertainties were also obtained using the sliding mode technique. The application of the achieved synchronization in secure communication is illustrated with the help of an example.

scholarly journals Numerical Analysis, Circuit Simulation, and Control Synchronization of Fractional-Order Unified Chaotic System

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1077 ◽  
Author(s):  
Li ◽  
Zhang ◽  
Yang
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Chaotic System ◽  
Decomposition Method ◽  
Design Theory ◽  
Control Method ◽  
Circuit Simulation ◽  
Adomian Decomposition Method ◽  
Unified Chaotic System ◽  
Adomian Decomposition

The traditional method of solving fractional chaotic system has the problem of low precision and is computationally cumbersome. In this paper, different fractional-order calculus solutions, the Adams prediction–correction method, the Adomian decomposition method and the improved Adomian decomposition method, are applied to the numerical analysis of the fractional-order unified chaotic system. The result shows that different methods have higher precision, smaller computational complexity, and shorter running time, in which the improved Adomian decomposition method works best. Then, based on the fractional-order chaotic circuit design theory, the circuit diagram of fractional-order unified chaotic system is designed. The result shows that the circuit simulation diagram of fractional-order unified chaotic system is basically consistent with the phase space diagram obtained from the numerical solution of the system, which verifies the existence of the fractional-order unified chaotic system of 0.9-order. Finally, the active control method is used to control and synchronize in the fractional-order unified chaotic system, and the experiment result shows that the method can achieve synchronization in a shorter time and has a better control performance.

scholarly journals Adaptive synchronization of the fractional-order unified chaotic system

2009 ◽  
Vol 58 (9) ◽  
pp. 6039
Author(s):  
Zhang Ruo-Xun ◽  
Yang Yang ◽  
Yang Shi-Ping
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Adaptive Synchronization ◽  
Unified Chaotic System
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