Dynamical analysis,circuit realization,and application in pseudorandom number generators of a fractional-order laser chaotic system

A new five-dimensional fractional-order laser chaotic system (FOLCS) is constructed by incorporating complex variables and fractional calculus into a Lorentz-Haken-type laser system. Dynamical behavior of the system, circuit realization and application in pseudorandom number generators are studied. Many types of multi-stable states are discovered in the system. Interestingly, there are two types of state transition phenomena in the system, one is the chaotic state degenerates to a periodical state, and the other is the intermittent chaotic oscillation. In addition, the complexity of the system when two parameters change simultaneously is measured by the spectral entropy algorithm. Moreover, a digital circuit is design and the chaotic oscillation behaviors of the system are verified on this circuit. Finally, a pseudo-random sequence generator is designed using the FOLCS, and the statistical characteristics of the generated pseudo-random sequence are tested with the NIST-800-22. This study enriches the research on the dynamics and applications of FOLCS.     

Hankel convolution operators on entire functions and distributions

In this paper we study the Hankel convolution operators on the space of even and entire functions and on Schwartz distribution spaces. We characterize the Hankel convolution operators as those ones that commute with Hankel translations and with a Bessel operator. Also we prove that the Hankel convolution operators are hypercyclic and chaotic on the spaces under consideration.     

GAUSSIAN WHITE NOISE CALCULUS OF GENERALIZED EXPANSION

A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators dt and its dual, creation operators t*.     

Time Series Prediction Based on Chaotic Attractor

A new prediction technique is proposed for chaotic time series. The usefulness of the technique is thatit can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. Atime-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the timeevolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate thelocal dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is testedfor the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this predictiontechnique can improve the prediction of chaotic time series.     

Fast algorithms for determining the linear complexities of sequences over GF(pm) with the period 3n

In this paper, for the the primes p such that 3 is a divisor of p − 1, we prove a result which reduces the computation of the linear complexity of a sequence over GF(p ^m) (any positive integer m) with the period 3n (n and p ^m − 1 are coprime) to the computation of the linear complexities of three sequences with the period n. Combined with some known algorithms such as generalized Games-Chan algorithm, Berlekamp-Massey algorithm and Xiao-Wei-Lam-Imamura algorithm, we can determine the linear complexity of any sequence over GF(p ^m) with the period 3n (n and p ^m − 1 are coprime) more efficiently.     

An improved algorithm for computing topological entropy

A new algorithm is presented for computing the topological entropy of a unimodal map of the interval. The accuracy of the algorithm is discussed and some graphs of the topological entropy which are obtained using the algorithm are displayed.     

一类不确定混沌系统的观测器同步

基于降维观测器的方法实现了一类具有外部扰动的混沌系统的同步. 无需知道系统外部扰动项的任何信息，就可对驱动系统设计基于降维观测器的响应系统，从而实现了混沌系统的同步. 数值仿真表明该方法是有效的. 关键词： 混沌同步 混沌系统 观测器     

基于改善空间关联性的混沌控制

基于混沌信号的统计特性，提出了一种通过改善混沌信号的空间关联性实现混沌控制的方法.以Hénon离散混沌系统和四阶Chua's电路超混沌连续系统为例进行了数值研究，验证了这种控制方法的有效性.结果表明， 通过改善混沌信号之间的空间关联性， 混沌系统能以较快的速度收敛到它的平衡点或多种周期轨道. 关键词： 混沌控制 空间关联性 Hénon系统 四阶Chua's电路     

一个新的四维混沌系统理论分析与电路实现

分析了一个新的复杂的四维混沌系统的基本特性，该系统每个方程中包含一个三次交叉乘积项，共有9个平衡点，它们相对于原点和坐标轴具有完美的对称性，并且相对于线性特性和不变流形具有很好的相似性.描述了两个同时共存的对称双翼吸引子.最后，设计了一个模拟电路来实现这个新的四维混沌系统，表明数值仿真和电路实现具有很好的一致性，同时说明在应用上由于频率不同导致的仿真与物理实现之间的重要区别. 关键词： 四维混沌系统 Lyapunov 指数 共存双翼吸引子 电路实现     

Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.