Finite-time sliding mode synchronization of chaotic systems

A new finite-time sliding mode control approach is presented for synchronizing two different topological structure chaotic systems. With the help of the Lyapunov method, the convergence property of the proposed control strategy is discussed in a rigorous manner. Furthermore, it is mathematically proved that our control strategy has a faster convergence speed than the conventional finite-time sliding mode control scheme. In addition, the proposed control strategy can ensure the finite-time synchronization between the master and the slave chaotic systems under internal uncertainties and external disturbances. Simulation results are provided to show the speediness and robustness of the proposed scheme. It is worth noticing that the proposed control scheme is applicable for secure communications.     

蔡氏对偶混沌电路分析

提出了一个新颖的蔡氏对偶混沌电路,并进行了深入的理论研究和计算机仿真分析.得出了几点结论:1)此混沌电路元器件少,且与蔡氏混沌电路结构完全对偶.2)在确定的元器件参数条件下,电路出现双涡卷奇怪吸引子和丰富的混沌动力学行为. 关键词： 蔡氏对偶电路 奇怪吸引子 混沌     

Control and synchronization of a hyperchaotic system based on passive control

In this paper, a new hyperchaotic system is proposed, and the basic properties of this system are analyzed by means of the equilibrium point, a Poincar map, the bifurcation diagram, and the Lyapunov exponents. Based on the passivity theory, the controllers are designed to achieve the new hyperchaotic system globally, asymptotically stabilized at the equilibrium point, and also realize the synchronization between the two hyperchaotic systems under different initial values respectively. Finally, the numerical simulation results show that the proposed control and synchronization schemes are effective.     

Controlling and synchronization of a hyperchaotic system based on passive control

In this paper, a new hyperchaotic system is proposed, and the basic properties of this system are analyzed by means of equilibrium point, Poincaré map, bifurcation diagram, and Lyapunov exponents. Based on the passivity theory, the controllers are designed to achieve the new hyperchaotic system globally, asymptotically stabilized at the equilibrium point, and also realize the synchronization between the two hyperchaotic systems under different initial values respectively. Finally, the numerical simulation results show that the proposed control and synchronization schemes are effective.     

A fractional order hyperchaotic system derived from Liu system and its circuit realization

In this paper we propose a novel four-dimensional fractional order hyperchaotic system derived from Liu system. Electronics workbench (EWB) and Matlab simulations show the dynamical behavior of the proposed four-dimensional fractional order hyperchaotic system. Finally, after separately using EWB and Matlab, an electronic circuit is designed to realize the novel four-dimensional fractional order hyperchaotic system and the experimental circuit results are obtained which are identical to software simulations.     

Experimental confirmation of a new reversed butterfly-shaped attractor

This paper reports a new reverse butterfly-shaped chaotic attractor and its experimental confirmation. Some basic dynamical properties, and chaotic behaviours of this new reverse butterfly attractor are studied. Simulation results support brief theoretical derivations. Furthermore, the system is experimentally confirmed by a simple electronic circuit.     

Realization of fractional-order Liu chaotic system by circuit

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.     

Demodulation of acoustic telemetry binary phase shift keying signal based on high-order Duffing system

In order to grasp the downhole situation immediately, logging while drilling(LWD) technology is adopted. One of the LWD technologies, called acoustic telemetry, can be successfully applied to modern drilling. It is critical for acoustic telemetry technology that the signal is successfully transmitted to the ground. In this paper, binary phase shift keying(BPSK) is used to modulate carrier waves for the transmission and a new BPSK demodulation scheme based on Duffing chaos is investigated. Firstly, a high-order system is given in order to enhance the signal detection capability and it is realized through building a virtual circuit using an electronic workbench(EWB). Secondly, a new BPSK demodulation scheme is proposed based on the intermittent chaos phenomena of the new Duffing system. Finally, a system variable crossing zero-point equidistance method is proposed to obtain the phase difference between the system and the BPSK signal. Then it is determined that the digital signal transmitted from the bottom of the well is ‘0' or ‘1'. The simulation results show that the demodulation method is feasible.     

Liu混沌系统的混沌分析及电路实验的研究

研究了一种新型混沌系统——Liu混沌系统的基本动力学行为以及电路实现的问题，给出了相图、庞卡莱映射、功率谱以及李雅普诺夫指数，基于李雅普诺夫指数谱和分叉图分析了系统参数对Liu混沌系统的影响.最后设计硬件电路证实了Liu混沌系统以及Liu混沌系统随系统参数变化时的各种状态的存在.给出数值仿真和电路实验的结果. 关键词： Liu混沌系统 分岔 电路实验     

四维系统中多涡卷混沌吸引子的仿真研究

通过构造一个新的非线性函数，研究一种新型四维系统多涡卷混沌信号发生器，这种多涡卷混沌信号发生器的主要特征是随着自然数n的增加，能产生2n+2个多涡卷混沌吸引子，通过改变控制参数k可以改变多涡卷混沌吸引子的混沌边界.并在EWB平台上设计了具体的电路，进行仿真实验验证. 关键词： 四维混沌系统 多涡卷混沌吸引子 非线性函数