A strong law of large numbers for random biased connected graphs

We consider a class of random connected graphs with random vertices and random edges in which the randomness of the vertices is determined by a continuous probability distribution and the randomness of the edges is determined by a connection function. We derive a strong law of large numbers on the total lengths of all random edges for a random biased connected graph that is a generalization of a directed k-nearest-neighbor graph.     

Linear combination rule in genetic algorithm for optimization of finite impulse response neural network to predict natural chaotic time series

A finite impulse response neural network, with tap delay lines after each neuron in hidden layer, is used. Genetic algorithm with arithmetic decimal crossover and Roulette selection with normal probability mutation method with linear combination rule is used for optimization of FIR neural network. The method is applied for prediction of several important and benchmarks chaotic time series such as: geomagnetic activity index natural time series and famous Mackey–Glass time series. The results of simulations shows that applying dynamic neural models for modeling of highly nonlinear chaotic systems is more satisfactory with respect to feed forward neural networks. Likewise, global optimization method such as genetic algorithm is more efficient in comparison of nonlinear gradient based optimization methods like momentum term, conjugate gradient.     

Synchronization for fractional‐order multi‐linked complex network with two kinds of topological structure via periodically intermittent control

This paper concentrates on the global synchronization of the fractional‐order multi‐linked complex network (FMCN) via periodically intermittent control. It should be stressed that periodically intermittent control is employed to the FMCN for the first time. Moreover, the network is defined on digraphs with different weights, and two situations on topological structure of the network are discussed, including each digraph being strongly connected, and the biggest one being strongly connected. Based on Lyapunov method and graph theory, some synchronization criteria are obtained under two situations. And, the obtained synchronization criteria have a close relationship with the order of fractional‐order derivative, coupling strength, control gain, control rate, and control period. Besides, for practicability, theoretical results are applied to studying the synchronization of fractional‐order multi‐linked chaotic systems, and some sufficient conditions are provided. For a special case, fractional‐order multi‐linked Lorenz chaotic systems, numerical simulations are given to indicate the feasibility of theoretical results and the effectiveness of control strategy.     

Suppressing chaos of a complex Duffing's system using a random phase

The effect of random phase for a complex Duffing's system is investigated. We show as the intensity of random noise properly increases the chaotic dynamical behavior will be suppressed by the criterion of top Lyapunov exponent, which is computed based on the Khasminskii's formulation and the extension of Wedig's algorithm for linear stochastic systems. Also Poincaré map analysis, phase plot and the time evolution are carried out to confirm the obtained results of Lyapunov exponent on dynamical behavior including the stability, bifurcation and chaos. Thus excellent agreement between these results is found.     

Effect of random parameter switching on commensurate fractional order chaotic systems

The paper explores the effect of random parameter switching in a fractional order (FO) unified chaotic system which captures the dynamics of three popular sub-classes of chaotic systems i.e. Lorenz, Lu and Chen's family of attractors. The disappearance of chaos in such systems which rapidly switch from one family to the other has been investigated here for the commensurate FO scenario. Our simulation study show that a noise-like random variation in the key parameter of the unified chaotic system along with a gradual decrease in the commensurate FO is capable of suppressing the chaotic fluctuations much earlier than that with the fixed parameter one. The chaotic time series produced by such random parameter switching in nonlinear dynamical systems have been characterized using the largest Lyapunov exponent (LLE) and Shannon entropy. The effect of choosing different simulation techniques for random parameter FO switched chaotic systems have also been explored through two frequency domain and three time domain methods. Such a noise-like random switching mechanism could be useful for stabilization and control of chaotic oscillation in many real-world applications.     

A linearization based non-iterative approach to measure the gaussian noise level for chaotic time series

In this work we propose a non-iterative method to determine the noise level of chaotic time series. For this purpose, we use the gaussian noise functional derived by Schreiber in 1993. It is shown that the noise function could be approximated by a stretched exponential decay form. The decay function is then used to construct a linear least squares approach where global solution exists. We have developed a software basis to calculate the noise level which is based on TISEAN algorithms. A practical way to exclude the outlying observations for small length scales has been proposed to prevent estimation bias. The algorithm is tested on well known chaotic systems including Henon, Ikeda map and Lorenz, Rössler, Chua flow data. Although the results of the algorithm obtained from simulated discrete dynamics are not satisfactory, we have shown that it performs well on flow data even for extreme level of noise. The results that are obtained from the real world financial and biomedical time series have been interpreted.     

A directed weighted complex network for characterizing chaotic dynamics from time series

We propose a reliable method for constructing a directed weighted complex network (DWCN) from a time series. Through investigating the DWCN for various time series, we find that time series with different dynamics exhibit distinct topological properties. We indicate this topological distinction results from the hierarchy of unstable periodic orbits embedded in the chaotic attractor. Furthermore, we associate different aspects of dynamics with the topological indices of the DWCN, and illustrate how the DWCN can be exploited to detect unstable periodic orbits of different periods. Examples using time series from classical chaotic systems are provided to demonstrate the effectiveness of our approach.     

Chaotic hash function based on circular shifts with variable parameters

We propose a chaotic hash algorithm based on circular shifts with variable parameters in this paper. We exploit piecewise linear chaotic map and one-way coupled map lattice to produce initial values and variable parameters. Circular shifts are introduced to improve the randomness of hash values. We evaluate the proposed hash algorithm in terms of distribution of the hash value, sensitivity of the hash value to slight modifications of the original message and secret keys, confusion and diffusion properties, robustness against birthday and meet-in-the-middle attacks, collision tests, analysis of speed, randomness tests, flexibility, computational complexity, and the results demonstrate that the proposed algorithm has strong security strength. Compared with the existing chaotic hash algorithms, our algorithm shows moderate statistical performance, better speed, randomness tests, and flexibility.     

Modified multiscale permutation entropy algorithm and its application for multiscroll chaotic systems

To analyze the complexity of continuous chaotic systems better, the modified multiscale permutation entropy (MMPE) algorithm is proposed. Characteristics and parameter choices of the MMPE algorithm are investigated. The comparative study between MPE and MMPE shows that MMPE has better robustness for identifying different chaotic systems when the scale factor τ takes large values. Compared with MPE, MMPE algorithm is more suitable for analyzing the complexity of time series as it has τ time series. For its application, MMPE algorithm is used to calculate the complexity of multiscroll chaotic systems. Results show that complexity of multiscroll chaotic systems does not increase as scroll number increases. Discussions based on first‐order difference operation present a reasonable explanation on why the complexity does not increase. This complexity analysis method lays a theoretical as well as experimental basis for the applications of multiscroll chaotic systems. © 2014 Wiley Periodicals, Inc. Complexity 21: 52–58, 2016     

Hybrid synchronization of heterogeneous chaotic systems on dynamic network

For researching the hybrid synchronization of heterogeneous chaotic systems on the complex dynamic network, there are two important issues to be discussed and analyzed. One is how to build a dynamic complex network which the connection between nodes is dynamic. Another is comparing and analyzing the synchronization characteristics of heterogeneous chaotic systems on the dynamic and static complex network. In this paper, the theoretical analysis and numerical simulation are implemented to study the synchronization on different dynamic and static complex networks. The results indicate it is feasible to realize the hybrid synchronization of heterogeneous chaotic systems on the complex dynamic network.     

Self-shrinking chaotic stream ciphers

In the last two decades, a growing number of chaos-based cipher systems have been suggested for use in cryptographic applications. Most of these systems were subject to cryptanalytic attacks, and many of them were shown to suffer from a lack of security. In this paper, we export the self-shrinking technique used in classical cryptography into chaotic systems to develop chaotic keystream generators capable of generating keystreams featuring very good statistical properties, and possessing high level of security. This paper proposes a sample self-shrinking chaos-based keystream generator implemented using a 1-D chaotic tent map. Randomness properties and results of statistical testing of keystream bits generated by applying the self-shrinking technique on chaotic maps with suitable parameters are found encouraging. Furthermore, chaotic cipher systems based on such technique are demonstrated to have a better performance in terms of randomness properties and security level than many existing cipher systems.     

Quasi‐randomness of graph balanced cut properties

Quasi‐random graphs can be informally described as graphs whose edge distribution closely resembles that of a truly random graph of the same edge density. Recently, Shapira and Yuster proved the following result on quasi‐randomness of graphs. Let k ≥ 2 be a fixed integer, α₁,…,α_k be positive reals satisfying \begin{align*}\sum_{i} \alpha_i = 1\end{align*} and (α₁,…,α_k)≠(1/k,…,1/k), and G be a graph on n vertices. If for every partition of the vertices of G into sets V ₁,…,V _k of size α₁n,…,α_kn, the number of complete graphs on k vertices which have exactly one vertex in each of these sets is similar to what we would expect in a random graph, then the graph is quasi‐random. However, the method of quasi‐random hypergraphs they used did not provide enough information to resolve the case (1/k,…,1/k) for graphs. In their work, Shapira and Yuster asked whether this case also forces the graph to be quasi‐random. Janson also posed the same question in his study of quasi‐randomness under the framework of graph limits. In this paper, we positively answer their question. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011     

Parameter estimation for noisy chaotic systems based on an improved particle swarm optimization algorithm

It is of great importance to estimate the unknown parameters and time delays of chaotic systems in control and synchronization. This paper is concerned with the uncertain parameters and time delays of chaotic systems corrupted with random noise. Parameters and time delays of such chaotic systems are estimated based on the improved particle swarm optimization algorithm for its global searching ability. Numerical simulations are given to show satisfactory results.     

Designing Network Encryption Machine Based on Henon Chaotic Key Algorithm

Nowadays, embedded network products are widely used in various technological fields. However, when such products are used, the transmission of network data could not be guaranteed with high security. To address the issue, this paper designed a network encryption machine based on S3C6410 processor and DM9000 Ethernet controller. The hardware circuit of this encryption machine is designed and developed with conciseness and stability. In software design, an improved algorithm of chaotic encryption based on Henon mapping is proposed. The algorithm overcomes the shortcoming in combining Logistic and Tent chaotic sequences. Moreover, the paper demonstrates some comparative experiments about autocorrelation and randomness. The results indicate that the new algorithm based on Henon chaotic sequences has a good performance in safety and is able to meet the requirements of confidential communications.     

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There're about 10^{11} neurons in the human brain.Through the synaptic junction, neurons have formed a highly complex network.And it is really important to figure out the information expressed in the network, which will contribute to the resolution of the prevention and diagnosis of cognitive disorder of human beings. This paper uses the schizophrenia and healthy controlled subjects' fMRI data to construct the brain network model, in order to explores abnormal topological properties of schizophrenics' brain network based on graph theory. When studying the human brain network information traditionally by the basement of graph theory, it's all assure that the human brain network model has invariance, so it takes the whole period of time series data in constructing human network model, which is a kind static network. However, it's hard to ensure this because of the nonstationarity of fMRI functional time series data. Thus, when constructing human brain network model, we should take its time-variation into consideration, then construct a dynamic brain network. We can explore the brain network information better. In this research, we segment the time series data, using time windows, to constructing dynamic brain network model, then analyze it combined with the knowledge of graph theory, thereby reducing effects that the nonstationarity of fMRI functional time series data will have. Comparing dynamic brain network of the schizophrenic patients with normal controls subjects' in different level, the results show that there are difference in single node property, group network property of schizophrenic patients and normal control subjects' whole brain dynamic functional connectivity network. The discovery of these difference in network topological properties has provide new clues for the further study on the pathological mechanism of schizophrenia.     

风险应对视角下不确定需求定位-路径鲁棒优化研究

及时准确地配送应急救援物资是突发公共事件救援过程中的关键环节,综合考虑应急救援过程中出现的需求随机性,路网的连通能力下降和设施点失灵等情况,采用车辆与直升机联合运输方式进行配送,以应急系统中各物资需求点的救援时间满意度之和最大、系统总成本最小及物资到达需求点的救援时间之和最小为目标,对多式联运三级网络应急物流系统定位—路径优化问题进行研究,建立了多目标定位—路径模型,并改进了遗传算法。最后,以汶川地震应急救援相关数据为例,对模型和算法的有效性进行了数据仿真验证,通过实验结果的对比分析,证明了鲁棒优化方法在处理不确定需求和设施失灵风险方面的有效性,进而为抵御突发公共事件发生后出现的风险,为解决突发公共事件发生后救援物资的安全及时准确配送提供了有效的方法。     

Leaderless and leader-following consensus of multi-agent chaotic systems with unknown time delays and switching topologies

In this paper the distributed consensus problem for a class of multi-agent chaotic systems with unknown time delays under switching topologies and directed intermittent communications is investigated. Each agent is modeled as a general nonlinear system including many chaotic systems with or without time delays. Based on the Lyapunov stability theory and graph theory, some sufficient conditions guarantee the exponential convergence. A graph-dependent Lyapunov proof provides the definite relationship among the bound of unknown time delays, the admissible communication rate and each possible topology duration. Moreover, the relationship reveals that these parameters have impacts on both the convergence speed and control cost. The case with leader-following communication graph is also addressed. Finally, simulation results verify the effectiveness of the proposed method.     

The Queueing Maximal availability location problem: A model for the siting of emergency vehicles

The Maximal Availability Location Problem (MALP) has been recently formulated as a probabilistic version of the maximal covering location problem. The added feature in MALP is that randomness into the availability of servers is considered. In MALP, though, it is assumed that the probabilities of different servers being busy are independent. In this paper, we utilize results from queuing theory to relax this assumption, obtaining a more realistic model for emergency systems: the Queueing MALP or Q-MALP. We also consider in this model that travel times or distances along arcs of the network are random variables. We show here how to site limited numbers of emergency vehicles, such as ambulances, in such a way as to maximize the calls for service which have an ambulance available within a time or distance standard with reliability α — using a queueing theory model for server availability. We also propose some extensions to the basic model. Formulations are presented and computational experience is offered.     

复杂多卷波混沌系统的理论设计与电路实现

双卷波Chua电路的发明第一次在混沌理论与非线性电路之间建立了直接联系.复杂多卷波混沌系统在混沌理论与非线性电路之间架起了桥梁.复杂多卷波混沌系统具有明确的工程应用背景,它的理论设计与电路实现在过去三十年里得到迅猛发展.本文简要的回顾国内外过去三十年在复杂多卷波混沌系统的理论设计与电路实现上的主要研究进展,包括基本理论,设计方法与典型的工程应用,试图推进国内复杂多卷波混沌系统的研究.     

基于混合模型的原油价格混沌预测方法

针对原油现货价格的非线性和时变性特征,提出一种小波变换结合Elman神经网络和广义自回归条件异方差(GARCH)模型的混沌预测方法。首先利用小波变换将原油现货价格序列分解和重构成概貌序列和细节序列。其次对概貌序列和原油期货价格序列进行相空间重构,建立Elman神经网络的混沌时间序列模型预测概貌序列的未来值;同时以细节序列为历史数据,构建GARCH模型预测细节序列的未来值;最后将概貌序列和细节序列的未来值求和作为最终的预测值。实验证明该方法能够提供更准确的预测结果。