Decentralized state-feedback chaotification method of discrete Takagi-Sugeno fuzzy systems

A new chaotification method is proposed for making an arbitrarily given discrete Takagi-Sugeno (TS) fuzzy system chaotic. Based on a given discrete TS fuzzy system, the new chaotification method uses the decentralized state-feedback control and the continuous sawtooth function, instead of the modulo operation, to construct a chaotic nonlinear system,which can generate discrete chaos with the arbitrarily desired amplitude bound. We apply the improved Marotto theorem to mathematically prove that the controlled system is chaotic in the sense of Li and Yorke. In particular, an explicit formula for the computation of chaotification parameters is obtained. A numerical example is used to illustrate the theoretical results.     

Chaos communication based on synchronization of discrete-time chaotic systems

A novel chaos communication method is proposed based on synchronization of discrete-time chaotic systems. This method uses a full-order state observer to achieve synchronization and secure communication between the transmitter and the receiver. Further, we present a multiple-access chaotic digital communication method by combining the observer with the on-line least square method. Simulation results are also given for illustration.     

Analysing chaos in fractional-order systems with the harmonic balance method

In this paper, the fractional-order Genesio--Tesi system showing chaotic behaviours is introduced, and the corresponding one in an integer-order form is studied intensively. Based on the harmonic balance principle, which is widely used in the frequency analysis of nonlinear control systems, a theoretical approach is used to investigate the conditions of system parameters under which this fractional-order system can give rise to a chaotic attractor. Finally, the numerical simulation is used to verify the validity of the theoretical results.     

盐水-水的小孔周期性泄流实验与分析

通过对盐水-水小孔周期性泄流的实验研究,对孔径为1.32 mm的8种不同孔长进行测量,得出周期正比于孔长的1.1±0.1次方,同时对孔径为1.32 mm孔长为113.00 mm条件下的内筒液面跟踪记录得出实验曲线为指数形式,与理论分析符合得较好.     

Chaotifying a stable linear controllable system by single input state feedback

In this paper, an approach for chaotifying a stable controllable linear system via single input state-feedback is presented. The overflow function of the system states is designed as the feedback controller, which can make the fixed point of the closed-loop system to be a snap-back repeller, thereby yields chaotic dynamics. Based on the Marotto theorem, it proves theoretically that the closed-loop system is chaotic in the sense of Li and Yorke. Finally, the simulation results are used to illustrate the effectiveness of the proposed method.     

A new output feedback synchronization theorem for a class of chaotic systems with a scalar transmitted signal

This paper proposes a new, simple and yet applicable output feedback synchronization theorem for a large class of chaotic systems. We take a linear combination of drive system state variables as a scale-driving signal. It is proved that synchronization between the drive and the response systems can be obtained via a simple linear output error feedback control. The linear feedback gain is a function of a free parameter. The approach is illustrated using the R\"{o}ssler hyperchaotic systems and Chua's chaotic oscillators.     

Chaotic dynamics of the fractional-order Ikeda delay system and its synchronization

In this paper we numerically investigate the chaotic behaviours of the fractional-order Ikeda delay system. The results show that chaos exists in the fractional-order Ikeda delay system with order less than 1. The lowest order for chaos to be able to appear in this system is found to be 0.1. Master--slave synchronization of chaotic fractional-order Ikeda delay systems with linear coupling is also studied.     

汽油与酒精自动交换的周期性分层振荡的实验研究

探究了汽油与酒精之间周期性振荡交换,实验得知汽油与酒精之间能产生周期性振荡现象,且内外筒溶液具有明显的分层现象,得到振荡周期与孔长和孔径关系为T∝L1/d4的实验结论;内筒初始酒精液面高度几乎不影响振荡周期,定性研究内筒酒精液面高度变化与孔长、周期次序的关系,最后给出在两不稳定平衡点间内液面位置变化量的表达式.     

通过分散反馈控制使稳定的Takagi-Sugeno(TS)模糊系统产生Devaney混沌

研究了利用分散状态反馈控制使稳定的Takagi-Sugeno(TS)模糊系统产生Devaney混沌的问题。所提的分散反馈控制器是由分散线性反馈控制器与2补运算的溢出非线性函数复合而成的。2补运算的溢出非线性导致了复杂动态。应用Shi-Chen定理从数学上证明了受控系统在Devaney意义下确实是混沌的。给出了计算混沌化参数的解析公式。一个数值例子被用来说明所提的理论结果。     

利用锯齿非线性混沌化稳定的Takagi-Sugeno (TS) 模糊系统

研究了利用任意小幅值的状态反馈控制来混沌化稳定的Takagi-Sugeno (TS) 模糊系统问题。所用状态反馈控制器是系统状态的锯齿函数。我们应用改进的Marotto定理从数学上证明了受控系统在Li-Yorke意义下是混沌的。特别地，给出了计算混沌化参数的解析公式。最后一个数值例子被用来说明所提的理论结果。