Dynamic behavior of fractional order Duffing chaotic system and its synchronization via singly active control

With the increasingly deep studies in physics and technology,the dynamics of fractional order nonlinear systems and the synchronization of fractional order chaotic systems have become the focus in scientific research.In this paper,the dynamic behavior including the chaotic properties of fractional order Duffing systems is extensively investigated.With the stability criterion of linear fractional systems,the synchronization of a fractional non-autonomous system is obtained.Specifically,an effective singly active control is proposed and used to synchronize a fractional order Duffing system.The numerical results demonstrate the effectiveness of the proposed methods.     

分数阶Duffing混沌系统的动力性态及其由单一主动控制的混沌同步

随着物理与技术的深入研究,分数阶非线性系统的动力性态及其分数阶混沌系统的同步成为研究的焦点.研究了分数阶Duffing系统的动力性态包括混沌性质,并且由分数阶非线性稳定性准则得到了分数阶非自治系统的混沌同步.特别地,研究了由单一主动控制的分数阶Duffing系统的同步.相应的数值结果演示了方法的有效性.     

Wavelet threshold method of resolving noise interference in periodic short-impulse signals chaotic detection

The chaotic oscillator has already been considered as a powerful method to detect weak signals,even weak signals accompanied with noises.However,many examples,analyses and simulations indicate that chaotic oscillator detection system cannot guarantee the immunity to noises(even white noise).In fact the randomness of noises has a serious or even a destructive effect on the detection results in many cases.To solve this problem,we present a new detecting method based on wavelet threshold processing that can detect the chaotic weak signal accompanied with noise.All theoretical analyses and simulation experiments indicate that the new method reduces the noise interferences to detection significantly,thereby making the corresponding chaotic oscillator that detects the weak signals accompanied with noises more stable and reliable.     

Locale的仿紧完全正则反射

1972年, Isbell利用locale中由正规覆盖构成的一致结构的完备化, 证明了仿紧完全正则locale范畴是locale范畴的满反射子范畴. 本文通过在locale的补零元理想格上做核映射的方法, 给出locale的仿紧完全正则反射的明确构造, 并证明locale的仿紧完全正则反射是locale的 Stone-Čech紧化的子locale.     

拟连续Domain及其子范畴间的伴随关系

基于Smyth幂 Domain的构造,本文证明了连续半格范畴 CSL（分别地,有界完备连续Domain范畴CBD）是拟连续Domain范畴QCONT（分别地,Coherent拟连续 Domain范畴QCCOH）的反射子范畴.反例表明,连续 Domain范畴CONT作为范畴 QCONT的真子范畴并非其反射子范畴.所有结果均被进一步推广到拟代数Domain范畴.     

Urysohn引理与弧连通完全分配格

称一个完全分配格Ｌ满足Ｕｒｙｓｏｈｎ条件，如果对任一正规空间Ｘ及Ｘ的任意两个不交闭子集Ａ，Ｂ都有连续映射ｆ：Ｘ→Ｌ，使得ｆ［Ａ］＝｛０｝，ｆ［Ｂ］＝｛１｝，这里Ｌ赋予区间拓扑．本文证明了完全分配格Ｌ满足Ｕｒｙｓｏｈｎ条件当且仅当Ｌ弧连通，而Ｌ弧连通又等价于Ｌ有同构于单位区间Ｉ的极大链．     

Fractional backward Kolmogorov equations

This paper derives the fractional backward Kolmogorov equations in fractal space-time based on the construction of a model for dynamic trajectories. It shows that for the type of fractional backward Kolmogorov equation in the fractal time whose coefficient functions are independent of time, its solution is equal to the transfer probability density function of the subordinated process X(Sα(t)), the subordinator Sα(t) is termed as the inverse-time α-stable subordinator and the process X(τ) satisfies the corresponding time homogeneous Ito stochastic differential equation.     

FUZZY STONE-ECH COMPACTIFICATIONS AND THE LARGEST TYCHONOFF COMPACTIFICATIONS~(**)

Using the imbedding theory~([6]) and the N-compactness of L-fuzzy unit interval~([10]), the authors establish the Stone-ech compactification theory of Tychonoff spaces. As well known, the Stone-ech compactification in general topology is the largest compactification of all the Tychonoff compactifications. But this important property is not true in fuzzy topology. The process of the argument of this negative result is very helpful for establishing a more reasonable Stone-ech compactification theory~([12]). Moreover, as relative results, the metrization theorem of induced spaces and the structure of quasi-Boolean lattice seem to have independent interest.     

乘性二次噪声驱动的线性过阻尼振子的随机共振

针对乘性二次噪声和加性周期调制噪声联合驱动的线性过阻尼振子, 利用随机平均法推导了系统响应的一阶、 二阶稳态矩以及稳态响应振幅和方差的解析表达式. 理论分析和仿真实验均表明这类系统具有比传统的由线性噪声驱动的线性系统更丰富的动力学特性; 当二次噪声的系数满足一定条件时, 系统稳态响应的振幅及方差均存在广义随机共振现象.     

Control of a fractional chaotic system based on a fractional-order resistor-capacitor filter

We present a new fractional-order resistor-capacitor controller and a novel control method based on the fractional- order controller to control an arbitrary three-dimensional fractional chaotic system. The proposed control method is simple, robust, and theoretically rigorous, and its anti-noise performance is satisfactory. Numerical simulations are given for several fractional chaotic systems to verify the effectiveness and the universality of the proposed control method.