This paper addresses the adaptive synchronization for uncertain Liu system via a nonlinear input. By using a single nonlinear controller, the approach is utilized to implement the synchronization of Liu system with to...This paper addresses the adaptive synchronization for uncertain Liu system via a nonlinear input. By using a single nonlinear controller, the approach is utilized to implement the synchronization of Liu system with total parameters unknown. This method is simple and can be easily designed. What is more, it improves the existing conclusions in Ref [12]. Simulation results prove that the controller is effective and feasible in the end.展开更多
Based on the three-dimensional Liu system with a nonlinear term of square, this paper appends a state variable to the system, and further adds a driving signal of the sine signal to construct a novel 4-demensional non...Based on the three-dimensional Liu system with a nonlinear term of square, this paper appends a state variable to the system, and further adds a driving signal of the sine signal to construct a novel 4-demensional nonautonomous hyperchaotic Liu system. The appended variable is formed by the product of the nonlinear quadratic term of the original state variables and the driving signal. Through adjusting the frequency of the driving signal, the system can be controlled to show some different dynamic behaviors. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the novel systems are analyzed. Furthermore, the corresponding hardware circuits are implemented. Both the experimental results and the simulation results confirm that the method is feasible. The method, which adjusts the frequency of the input sine signal to control the system to show different dynamic behaviors, can make the dynamic property of the system become more complex, but easier to be controlled accurately as well.展开更多
This paper investigates the dynamical behaviour of the Liu system with time delayed feedback. Two typical situations are considered and the effect of time-delay parameter on the dynamics of the system is discussed. It...This paper investigates the dynamical behaviour of the Liu system with time delayed feedback. Two typical situations are considered and the effect of time-delay parameter on the dynamics of the system is discussed. It is shown that the Liu system with time delayed feedback may exhibit interesting and extremely rich dynamical behaviour. The evolution of the dynamics is shown to be complex with varying time-delay parameter. Moreover, the strange attractor like ‘wormhole＇ is detected via numerical simulations.展开更多
Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperc...Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.展开更多
In this paper, chaotic behaviours in the fractional-order Liu system are studied. Based on the approximation theory of fractional-order operator, circuits are designed to simulate the fractional- order Liu system with...In this paper, chaotic behaviours in the fractional-order Liu system are studied. Based on the approximation theory of fractional-order operator, circuits are designed to simulate the fractional- order Liu system with q=0.1 - 0.9 in a step of 0.1, and an experiment has demonstrated the 2.7-order Liu system. The simulation results prove that the chaos exists indeed in the fractional-order Liu system with an order as low as 0.3. The experimental results prove that the fractional-order chaotic system can be realized by using hardware devices, which lays the foundation for its practical applications.展开更多
A new circuit unit for the analysis and the synthesis of the chaotic behaviours in a fractional-order Liu system is proposed in this paper. Based on the approximation theory of fractional-order operator, an electronic...A new circuit unit for the analysis and the synthesis of the chaotic behaviours in a fractional-order Liu system is proposed in this paper. Based on the approximation theory of fractional-order operator, an electronic circuit is designed to describe the dynamic behaviours of the fractional-order Liu system with α = 0.9. The results between simulation and experiment are in good agreement with each other, thereby proving that the chaos exists indeed in the fractional-order Liu system.展开更多
In the paper, the Liu system with a feedback controller is discussed. The influence of the feedback coefficient of the controlled system is studied through Lyapunov exponents spectrum and bifurcation diagram. Various ...In the paper, the Liu system with a feedback controller is discussed. The influence of the feedback coefficient of the controlled system is studied through Lyapunov exponents spectrum and bifurcation diagram. Various attractors are demonstrated not only by numerical simulations but also by circuit experiments. Only one feedback channel is used in our study, which is useful in communication. The circuit experiments show that our study has significance in practical applications.展开更多
This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fra...This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fractal dimension and the hyperchaotic attractor evolving into chaotic, periodic, quasi-periodic dynamical behaviours by varying parameter d are studied briefly. Various attractors are illustrated not only by computer simulation but also by conducting an electronic circuit experiment.展开更多
An impulsive control scheme of Liu＇s system is presented in this paper. Some less conservative conditions with impulses at fixed times are provided, which can guarantee the global asymptotical stability and global ex...An impulsive control scheme of Liu＇s system is presented in this paper. Some less conservative conditions with impulses at fixed times are provided, which can guarantee the global asymptotical stability and global exponential stability for the impulsive control of Liu＇s systems. We also present the estimate of the stable region for the equidistance impulsive interval. Furthermore, an illustrative example is given to show the effectiveness of the proposed results.展开更多
A kind of synchronization controller for Liu chaotic systems whose nonlinear components are subject to Lipschitz condition was proposed. By using Lyapunov function and linear matrix inequality technique, a self-adapti...A kind of synchronization controller for Liu chaotic systems whose nonlinear components are subject to Lipschitz condition was proposed. By using Lyapunov function and linear matrix inequality technique, a self-adaptive synchronization controller was constructed for Liu chaotic systems. There are two components of our derived synchronization controller: linear and nonlinear component. Linear component is composed of errors of the state variables between driving-systems and responding-stems, and nonlinear component is a self-adaptive synchronization controller. a proof was given for proving the feasibility of this method, and numerical simulations of Liu chaotic systems show its effectiveness. Furthermore, this method can be applied to other chaotic systems, such as Chen systems, Lorenz systems, Chua systems and Rssler systems,etc.展开更多
The new taxation system has beenoperated smoothly and its positiveresults have become evident since Chinacarried out the reform of the taxation systemin 1994.This was said by Mr.Liu Zhongli,Finance Minister and Direct...The new taxation system has beenoperated smoothly and its positiveresults have become evident since Chinacarried out the reform of the taxation systemin 1994.This was said by Mr.Liu Zhongli,Finance Minister and Director-General ofthe State Administration of Taxation at apress conference recently.The new taxationsystem brought RMB100 billion more to theTreasury in 1994,and the figure is expectedto be bigger in 1995,he disclosed. The minister said that the state hasadopted an appropriately tight financial展开更多
利用三阶混沌系统构造了一种新的微弱信号检测系统——类Liu系统,对类Liu系统进行了深度的理论分析.类Liu系统中,当输入待测信号幅值大于某临界值时,系统可达到平衡点S0,S0中系统变量x平衡于摄动力信号,系统变量y,z收敛于零态,且S0对应...利用三阶混沌系统构造了一种新的微弱信号检测系统——类Liu系统,对类Liu系统进行了深度的理论分析.类Liu系统中,当输入待测信号幅值大于某临界值时,系统可达到平衡点S0,S0中系统变量x平衡于摄动力信号,系统变量y,z收敛于零态,且S0对应的Lyapunov指数小于零.通过Matlab仿真、Multisim电路仿真以及实际电路证明了类Liu系统的周期态收敛性及广域检测性,解决了传统Duffing系统进行微弱信号检测时周期态不收敛、只能进行窄域检测等问题,同时谱级信噪比范围仍可达-46.57 d B.类Liu系统采用了全新的设计理念,具有较高的实用价值,对未来海洋物联网中的水声通信有一定参考价值.展开更多
基金Project supported by the Educational Commission of Hubei Province of China,(Grant No 080056)
文摘This paper addresses the adaptive synchronization for uncertain Liu system via a nonlinear input. By using a single nonlinear controller, the approach is utilized to implement the synchronization of Liu system with total parameters unknown. This method is simple and can be easily designed. What is more, it improves the existing conclusions in Ref [12]. Simulation results prove that the controller is effective and feasible in the end.
基金supported by the National Natural Science Foundation of China (Grant No 60572089)the Natural Science Foundation of Chongqing (Grant No CSTC,2008BB2087)
文摘Based on the three-dimensional Liu system with a nonlinear term of square, this paper appends a state variable to the system, and further adds a driving signal of the sine signal to construct a novel 4-demensional nonautonomous hyperchaotic Liu system. The appended variable is formed by the product of the nonlinear quadratic term of the original state variables and the driving signal. Through adjusting the frequency of the driving signal, the system can be controlled to show some different dynamic behaviors. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the novel systems are analyzed. Furthermore, the corresponding hardware circuits are implemented. Both the experimental results and the simulation results confirm that the method is feasible. The method, which adjusts the frequency of the input sine signal to control the system to show different dynamic behaviors, can make the dynamic property of the system become more complex, but easier to be controlled accurately as well.
基金Project supported by the Science Foundation of Huazhong University of Science and Technology (Grant No 2006Q003B)
文摘This paper investigates the dynamical behaviour of the Liu system with time delayed feedback. Two typical situations are considered and the effect of time-delay parameter on the dynamics of the system is discussed. It is shown that the Liu system with time delayed feedback may exhibit interesting and extremely rich dynamical behaviour. The evolution of the dynamics is shown to be complex with varying time-delay parameter. Moreover, the strange attractor like ‘wormhole＇ is detected via numerical simulations.
基金Project supported by the National Natural Science Foundation of China (Grant No 60572089)the Natural Science Foundation of Chongqing (Grant No CSTC,2008BB2087)
文摘Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.
文摘In this paper, chaotic behaviours in the fractional-order Liu system are studied. Based on the approximation theory of fractional-order operator, circuits are designed to simulate the fractional- order Liu system with q=0.1 - 0.9 in a step of 0.1, and an experiment has demonstrated the 2.7-order Liu system. The simulation results prove that the chaos exists indeed in the fractional-order Liu system with an order as low as 0.3. The experimental results prove that the fractional-order chaotic system can be realized by using hardware devices, which lays the foundation for its practical applications.
文摘A new circuit unit for the analysis and the synthesis of the chaotic behaviours in a fractional-order Liu system is proposed in this paper. Based on the approximation theory of fractional-order operator, an electronic circuit is designed to describe the dynamic behaviours of the fractional-order Liu system with α = 0.9. The results between simulation and experiment are in good agreement with each other, thereby proving that the chaos exists indeed in the fractional-order Liu system.
文摘In the paper, the Liu system with a feedback controller is discussed. The influence of the feedback coefficient of the controlled system is studied through Lyapunov exponents spectrum and bifurcation diagram. Various attractors are demonstrated not only by numerical simulations but also by circuit experiments. Only one feedback channel is used in our study, which is useful in communication. The circuit experiments show that our study has significance in practical applications.
文摘This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fractal dimension and the hyperchaotic attractor evolving into chaotic, periodic, quasi-periodic dynamical behaviours by varying parameter d are studied briefly. Various attractors are illustrated not only by computer simulation but also by conducting an electronic circuit experiment.
基金Supported by Foundation of Zhejiang Educational Committee under Grant No. Y200805720
文摘An impulsive control scheme of Liu＇s system is presented in this paper. Some less conservative conditions with impulses at fixed times are provided, which can guarantee the global asymptotical stability and global exponential stability for the impulsive control of Liu＇s systems. We also present the estimate of the stable region for the equidistance impulsive interval. Furthermore, an illustrative example is given to show the effectiveness of the proposed results.
基金supported by the Science Foundation of Chongqing Education Department(KJ060506)Doctor Foundation of Chongqing University of Posts and Telecommunications(A2006-85)
文摘A kind of synchronization controller for Liu chaotic systems whose nonlinear components are subject to Lipschitz condition was proposed. By using Lyapunov function and linear matrix inequality technique, a self-adaptive synchronization controller was constructed for Liu chaotic systems. There are two components of our derived synchronization controller: linear and nonlinear component. Linear component is composed of errors of the state variables between driving-systems and responding-stems, and nonlinear component is a self-adaptive synchronization controller. a proof was given for proving the feasibility of this method, and numerical simulations of Liu chaotic systems show its effectiveness. Furthermore, this method can be applied to other chaotic systems, such as Chen systems, Lorenz systems, Chua systems and Rssler systems,etc.
文摘The new taxation system has beenoperated smoothly and its positiveresults have become evident since Chinacarried out the reform of the taxation systemin 1994.This was said by Mr.Liu Zhongli,Finance Minister and Director-General ofthe State Administration of Taxation at apress conference recently.The new taxationsystem brought RMB100 billion more to theTreasury in 1994,and the figure is expectedto be bigger in 1995,he disclosed. The minister said that the state hasadopted an appropriately tight financial
文摘利用三阶混沌系统构造了一种新的微弱信号检测系统——类Liu系统,对类Liu系统进行了深度的理论分析.类Liu系统中,当输入待测信号幅值大于某临界值时,系统可达到平衡点S0,S0中系统变量x平衡于摄动力信号,系统变量y,z收敛于零态,且S0对应的Lyapunov指数小于零.通过Matlab仿真、Multisim电路仿真以及实际电路证明了类Liu系统的周期态收敛性及广域检测性,解决了传统Duffing系统进行微弱信号检测时周期态不收敛、只能进行窄域检测等问题,同时谱级信噪比范围仍可达-46.57 d B.类Liu系统采用了全新的设计理念,具有较高的实用价值,对未来海洋物联网中的水声通信有一定参考价值.
