Special dynamic behaviors of a temporal chaotic system

When dynamic behaviors of temporal chaotic system are analyzed,we find that a temporal chaotic system has not only genetic dynamic behaviors of chaotic reflection,but also has phenomena influencing two chaotic attractors by original values.Along with the system parameters changing to certain value,the system will appear a break in chaotic region,and jump to another orbit of attractors.When it is opposite that the system parameters change direction,the temporal chaotic system appears complicated chaotic behaviors.     

Uniform random number generation

In typical stochastic simulations, randomness is produced by generating a sequence of independent uniform variates (usually real-valued between 0 and 1, or integer-valued in some interval) and transforming them in an appropriate way. In this paper, we examine practical ways of generating (deterministic approximations to) such uniform variates on a computer. We compare them in terms of ease of implementation, efficiency, theoretical support, and statistical robustness. We look in particular at several classes of generators, such as linear congruential, multiple recursive, digital multistep, Tausworthe, lagged-Fibonacci, generalized feedback shift register, matrix, linear congruential over fields of formal series, and combined generators, and show how all of them can be analyzed in terms of their lattice structure. We also mention other classes of generators, like non-linear generators, discuss other kinds of theoretical and empirical statistical tests, and give a bibliographic survey of recent papers on the subject.     

Design and circuit implementation for a novel charge-controlled chaotic memristor system

This paper deals with the simulation and implementation of a new charge-controlled memristor based on the simplest chaotic circuit. The circuit we used has only three basic elements in series. Some period-one and period-doubling chaotic routes are generated by this circuit with changes in its component values. Device-level simulation is conducted by using Multisim to provide the basis for building the real chaotic circuit. The results of numerical simulations are identical to those of circuit simulations, demonstrating that the circuit is feasible.     

常见随机数发生器的缺陷及组合随机数发生器的理论与实践

随机数是蒙特卡罗 Monte- Carlo方法的基础 .本文首先指出线性同余法和移位寄存器 (亦称 Tausworthe)序列等常见随机数发生器的一些缺陷 ;在此基础上介绍可产生具有优良品质随机数的组合发生器。本文既介绍理论结果 ,用以证明组合发生器确实可以优于单个发生器 ;也具体构造了几个可供实际使用的组合随机数发生器。严格而全面的统计检验表明 ,它们可以产生具有优良品质的随机数     

A feasible memristive Chua's circuit via bridging a generalized memristor

By bridging a generalized memristor between a passive $LC$ oscillator and an active $RC$ filter, a simple and feasible memristive Chua''s circuit is presented. The generalized memristor without grounded limitation is equivalently achieved by a full-wave rectifier cascaded with a first-order parallel $RC$ filter. The dynamical characteristics of the proposed circuit are investigated both theoretically and numerically, from which it can be found that the circuit has three unstable equilibrium points and demonstrates complex nonlinear phenomena. The experimental circuit is easy to implement and the measurement results validate the results of theoretical analyses.     

随机数及其在数据库中的应用

本文在分析随机数及其产生方法的基础上 ,介绍计算机产生随机数和随机抽样在数据库中应用的实现方法     

A new 4-D non-equilibrium fractional-order chaotic system and its circuit implementation

A new 4-D fractional-order chaotic system without equilibrium point is proposed in this paper. There is no chaotic behavior for its corresponding integer-order system. By computer simulations, we find complex dynamical behaviors in this system, and obtain that the lowest order for exhibiting a chaotic attractor is 3.2. We also design an electronic circuit to realize this 4-D fractional-order chaotic system and present some experiment results.     

On the chromatic number of a random 5‐regular graph

It was only recently shown by Shi and Wormald, using the differential equation method to analyze an appropriate algorithm, that a random 5‐regular graph asymptotically almost surely has chromatic number at most 4. Here, we show that the chromatic number of a random 5‐regular graph is asymptotically almost surely equal to 3, provided a certain four‐variable function has a unique maximum at a given point in a bounded domain. We also describe extensive numerical evidence that strongly suggests that the latter condition holds. The proof applies the small subgraph conditioning method to the number of locally rainbow balanced 3‐colorings, where a coloring is balanced if the number of vertices of each color is equal, and locally rainbow if every vertex is adjacent to at least one vertex of each of the other colors. © 2009 Wiley Periodicals, Inc. J Graph Theory 61: 157–191, 2009     

Nonlinear electronic circuit, Part II: synchronization in a chaotic MODEM scheme

In this work we present a thorough investigation of the effect of noise (internal or external) on the synchronization of a drive-response configuration system (unidirectional coupling between two identical systems). Moreover, since in every practical implementation of a communication system, the transmitter and receiver circuits (although identical) operate under slightly different conditions it is essential to consider the case of the mismatch between the parameters of the transmitter and the receiver. In our work we consider the non-autonomous 2nd order nonlinear oscillator system presented in [G. Mycolaitis, A. Tamasevicious, A. Cenys, A. Namajunas, K. Navionis, A. N. Anagnostopoulos, Globally synchronizable non-autonomous chaotic oscillator, in: Proc. of 7th International Workshop on Nonlinear Dynamics of Electronic Systems, Denmark, July 1999, pp. 277-280] which is particularly suitable for digital communications.Furthermore, we modified the previous chaotic communication system in order to exhibit enhanced security features. The enhancement in the security of the system is achieved by introducing a set of parameters used in the encoding and decoding of the message signal. We also introduce a time delay parameter in the dynamical system which on the one hand improves the chaotic behavior of the system and on the other hand, adds further security in the encoding-decoding scheme.     

The wavelet transform method applied to a coupled chaotic system with asymmetric coupling schemes

The wavelet transform method originated by Wei et al. (2002) [19] is an effective tool for enhancing the transverse stability of the synchronous manifold of a coupled chaotic system. Much of the theoretical study on this matter is centered on networks that are symmetrically coupled. However, in real applications, the coupling topology of a network is often asymmetric; see Belykh et al. (2006)  [23], [24], Chavez et al. (2005)  [25], Hwang et al. (2005)  [26], Juang et al. (2007)  [17], and Wu (2003)  [13]. In this work, a certain type of asymmetric sparse connection topology for networks of coupled chaotic systems is presented. Moreover, our work here represents the first step in understanding how to actually control the stability of global synchronization from dynamical chaos for asymmetrically connected networks of coupled chaotic systems via the wavelet transform method. In particular, we obtain the following results. First, it is shown that the lower bound for achieving synchrony of the coupled chaotic system with the wavelet transform method is independent of the number of nodes. Second, we demonstrate that the wavelet transform method as applied to networks of coupled chaotic systems is even more effective and controllable for asymmetric coupling schemes as compared to the symmetric cases.     

Pseudo-random number generator based on mixing of three chaotic maps

A secure pseudo-random number generator three-mixer is proposed. The principle of the method consists in mixing three chaotic maps produced from an input initial vector. The algorithm uses permutations whose positions are computed and indexed by a standard chaotic function and a linear congruence. The performance of that scheme is evaluated through statistical analysis. Such a cryptosystem lets appear significant cryptographic qualities for a high security level.     

The number of rooted circuit boundary maps

In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with two parameters; the size and the valency of the root-face, are also extracted.     

On the chromatic number of random graphs

We consider random graphs G_n,p with fixed edge-probability p. We refine an argument of Bollobás to show that almost all such graphs have chromatic number equal to n/{2 log_b n ? 2 log_b log_b n + O(1)} where b = 1/(1 ? p).     

Asymptotic Expansions for the Distribution of the Crossing Number of a Strip by Sample Paths of a Random Walk

The complete asymptotic expansions are obtained for the distribution of the crossing number of a strip in n steps by sample paths of an integer-valued random walk with zero mean. We suppose that the Cramer condition holds for the distribution of jumps and the width of strip increases together with n; the results are proven under various conditions on the width growth rate. The method is based on the Wiener–Hopf factorization; it consists in finding representations of the moment generating functions of the distributions under study, the distinguishing of the main terms of the asymptotics of these representations, and the subsequent inversion of the main terms by the modified saddle-point method.     

Extended-Kalman-filter-based chaotic communication

Together with the optimal linearization technique, an extended-Kalman-filter-basedchaotic communication is first proposed in this paper. First,the optimal linearization technique is utilized to find theexact linear models of the chaotic system at operating statesof interest. Then, an extended Kalman filter (EKF) algorithmis used to estimate both the parameters and states where themessage is already embedded. By using the EKF together withthe optimal linear model, the message can be recovered wellat the receiver's end. Numerical examples and simulations aregiven to show the effectiveness of the proposed methodology.     

一种基于线性同余算法的伪随机数产生器

线性同余算法作为使用最为广泛的伪随机数产生算法,具有产生速度快、输出序列周期长等特点,但安全性能不佳的弱点始终制约着该算法在密码学领域的应用.本文在对线性同余算法详细分析的基础上,给出了一种不受乘数a选择限制的伪随机数产生器.该算法具有良好的伪随机性和安全性.     

The influence of noise on a classical chaotic scatterer

A classical, chaotic scatterer consisting of three, equal-sized, equidistant hard discs, also known as the Gaspard–Rice system [Gaspard P, Rice SA. Scattering from a classically chaotic repellor. J Chem Phys 1989;90(4):2225–2241] is studied in the presence of white noise. The fractal dimension of the stable manifold is measured using the uncertainty fraction. The volume of the manifold, and thus of the invariant set, when considered in a possibilistic sense, is found to scale with the magnitude of the noise, thus extending the results of Ott et al. [Ott E, York ED, Yorke JA. A scaling law: How an attractors volume depends on noise level. Physica D 1985;16:62–78] from attracting to non-attracting sets.     

An application of deterministic chaotic maps to model packet traffic

We investigate the application of deterministic chaotic maps to model traffic sources in packet based networks, motivated in part by recent measurement studies which indicate the presence of significant statistical features in packet traffic more characteristic of fractal processes than conventional stochastic processes. We describe one approach whereby traffic sources can be modeled by chaotic maps, and illustrate the traffic characteristics that can be generated by analyzing several classes of maps. We outline a potential performance analysis approach based on chaotic maps that can be used to assess the traffic significance of fractal properties. We show that low order nonlinear maps can capture several of the fractal properties observed in actual data, and show that the source characteristics observed in actual traffic can lead to heavy-tailed queue length distributions. It is our conclusion that while there are considerable analytical difficulties, chaotic maps may allow accurate, yet concise, models of packet traffic, with some potential for transient and steady state analysis.     

Pseudo random number generator based on quantum chaotic map

For many years dissipative quantum maps were widely used as informative models of quantum chaos. In this paper, a new scheme for generating good pseudo-random numbers (PRNG), based on quantum logistic map is proposed. Note that the PRNG merely relies on the equations used in the quantum chaotic map. The algorithm is not complex, which does not impose high requirement on computer hardware and thus computation speed is fast. In order to face the challenge of using the proposed PRNG in quantum cryptography and other practical applications, the proposed PRNG is subjected to statistical tests using well-known test suites such as NIST, DIEHARD, ENT and TestU01. The results of the statistical tests were promising, as the proposed PRNG successfully passed all these tests. Moreover, the degree of non-periodicity of the chaotic sequences of the quantum map is investigated through the Scale index technique. The obtained result shows that, the sequence is more non-periodic. From these results it can be concluded that, the new scheme can generate a high percentage of usable pseudo-random numbers for simulation and other applications in scientific computing.