Cascades with coupled map lattices in preferential attachment community networks

In this paper, cascading failure is studied by coupled map lattice （CML） methods in preferential attachment community networks. It is found that external perturbation R is increasing with modularity Q growing by simulation. In particular, the large modularity Q can hold off the cascading failure dynamic process in community networks. Furthermore, different attack strategies also greatly affect the cascading failure dynamic process. It is particularly significant to control cascading failure process in real community networks.

Tolerance of edge cascades with coupled map lattices methods

This paper studies the cascading failure on random networks and scale-free networks by introducing the tolerance parameter of edge based on the coupled map lattices methods. The whole work focuses on investigating some indices including the number of failed edges, dynamic edge tolerance capacity and the perturbation of edge. In general, it assumes that the perturbation is attributed to the normal distribution in adopted simulations. By investigating the effectiveness of edge tolerance in scale-free and random networks, it finds that the larger tolerance parameter λ can more efficiently delay the cascading failure process for scale-free networks than random networks. These results indicate that the cascading failure process can be effectively controlled by increasing the tolerance parameter λ. Moreover, the simulations also show that, larger variance of perturbation can easily trigger the cascading failures than the smaller one. This study may be useful for evaluating efficiency of whole traffic systems, and for alleviating cascading failure in such systems.

Partial and complete periodic synchronization in coupled discontinuous map lattices

The partial and complete periodic synchronization in coupled discontinuous map lattices consisting of both discon- tinuous and non-invertible maps are discussed. We classify three typical types of periodic synchronization states, which give rise to different spatiotemporal patterns including static partial periodic synchronization, dynamically periodic syn- chronization, and complete periodic synchronization patterns. A special prelude dynamics of partial and complete periodic synchronization motion, which is shown by five separated concave curves in the time series plots of the order parameters, is observed. The detailed analysis shows that the special prelude dynamics is induced by the competition between two synchronized clusters, and the analytical expression for the corresponding order parameter is obtained.

A Cryptographic Scheme Based on Spatiotemporal Chaos of Coupled Map Lattices

我们基于联合地图格子(电流型逻辑) 的空间与时间的混乱建议一个密码的计划，它基于一次性的垫。秘密成员系统的结构决定在解密的进步在在电流型逻辑探索空间与时间的混乱的动态行为暗示进步。电流型逻辑的起始的条件的部分被彻底的搜索用作秘密钥匙的一把秘密钥匙，和恢复由于到在空间与时间的混乱的起始的条件的敏感是不可能的系统。特殊计划的软件实现是容易的。

Effects of Scale-Free Topological Properties on Dynamical Synchronization and Control in Coupled Map Lattices

在纸，我们学习效果没有规模(SF ) 在联合地图格子(电流型逻辑) 的动态同步和控制上的拓扑学。我们的策略是使用三个反馈控制方法，包括经常的反馈和推迟时间的反馈的二种类型，到到达需要的同步状态的网络节点的小部分。二控制分叉图诗句反馈力量分别地被获得。当￡线性地被增加，为第一推迟时间的反馈控制的批评反馈力量γ _ c 的值线性地被增加，这被发现。有 SF 的电流型逻辑失去同步，如果γ 】 γ _ c.Numerical 例子被举表明所有结果， intermittency 发生。

Synchronizing spatiotemporal chaos in the coupled map lattices using nonlinear feedback functions

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PERIODIC SOLUTIONS IN ONE-DIMENSIONAL COUPLED MAP LATTICES

It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systems whose behavior can be regarded as infinite array of coupled oscillators. A method for estimating the critical coupling strength below which these solutions with time period persist is given. For some particular nonlinear solutions with time period,exponential decay in space is proved.

A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics

Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices （CMLs）. It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence （CD）. Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-to- noise ratios （SNRs） are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors usiug symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems.

A method of estimating initial conditions of coupled map lattices based on time-varying symbolic dynamics

A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices （CMLs）. The presented method combines symbolic dynamics with time-varying control parameters to develop a time-varying scheme for estimating the initial condition of multi-dimensional spatiotemporal chaotic signals. The performances of the presented time-varying estimator in both noiseless and noisy environments are analysed and compared with the common time-invariant estimator. Simulations are carried out and the obtained results show that the proposed method provides an efficient estimation of the initial condition of each lattice in the coupled system. The algorithm cannot yield an asymptotically unbiased estimation due to the effect of the coupling term, but the estimation with the time-varying algorithm is closer to the Cramer-Rao lower bound （CRLB） than that with the time-invariant estimation method, especially at high signal-to-noise ratios （SNRs）.

Some Chaotic Properties of a Kind of Coupled Map Lattices

This paper is concerned with some chaotic properties of a kind of coupled map lattices, which is proposed by Kaneko. First, this research discussed the sensitivity, infinite sensitivity, transitivity, accessibility, densely Li-Yorke sensitivity and exact of coupled map lattices. Then, some sufficient conditions under which <img src="Edit_c0fc315a-d176-4c9e-9e41-5cb6bc6d679d.bmp" alt="" /> is Kato chaotic, positive entropy chaotic and Ruelle-Takens chaos are obtained.

Periodic Windows in Weakly Coupled Map Lattices

<Abstract>The periodic windows in weakly coupled map lattices with both diffusive and gradient couplings are studied. By using the mode analysis method,which reduces the behavior of the coupled systems to a few numbers of independent modes,we theoretically analyze the detailed structures of the periodic windows.We find that the gradient coupling greatly enlarges the width of the periodic windows,compared with the diffusive coupling.

A Self-synchronizing Stream Encryption Scheme Based on One-Dimensional Coupled Map Lattices

我们在场一个自我同步的溪流加密计划基于处于起始的条件与空间与时间的混乱，并且大复杂性和小骚乱的散开能力的必要特征作为一个模型被介绍的 onone 维的联合地图格子。到评估计划，一系列统计测试被采用，并且结果显示出密文的好随机看的自然。而且，我们使用我们的算法加密一幅灰度图象显示出关键敏感。

Control Chaos of a Unidirectionally Traffic Coupled Map Lattice Model

Spatiotemporal chaos is studied by using the unidirectional traffic coupled lattice model with hyperbolic tangent local map. The coupled map lattice (CML) model can simulate the complex traffic flow phenomenon which is similar to the traditional traffic flow model. The nonlinear feedback method is used to study the control of the chaotic system of the unidirectionally traffic coupled map lattice model. The stability of spatiotemporal chaos in the coupled map lattice is realized. The results of numerical simulation show that there is a relationship between control results and control parameters when controlling spatiotemporal chaos to a uniform stable state in a certain phase space compression parameter region.

A Secure Watermarking Algorithm Based on Coupled Map Lattice

Based on the nonlinear theory, a secure watermarking algorithm using wavelet transform and coupled map lattice is presented. The chaos is sensitive to initial conditions and has a good non-relevant correlation property, but the finite precision effect limits its application in practical digital watermarking system. To overcome the undesirable short period of chaos mapping and improve the security level of watermarking, the hyper-chaotic sequence is adopted in this algorithm. The watermark is mixed with the hyper-chaotic sequence and embedded in the wavelet domain of the host image. Experimental results and analysis are given to demonstrate that the proposed watermarking algorithm is transparent, robust and secure.

CONVECTIVE COUPLED MAP FOR SIMULATING SPATIOTEMPORAL CHAOS IN FLOWS

A coupled map lattices with convective nonlinearity or, for short, Convective Coupled Map (CCM) is proposed in this paper to simulate spatiotemporal chaos in fluid hows. It is found that the parameter region of spatiotemporal chaos can be determined by the maximal Liapunov exponent of its complexity time series. This simple model implies a similar physical mechanism for turbulence such that the route to spatiotemporal chaos in fluid hows can be envisaged.

A joint image compression and encryption scheme based on a novel coupled map lattice system and DNA operations

In this paper,an efficient image encryption scheme based on a novel mixed linear–nonlinear coupled map lattice(NMLNCML)system and DNA operations is presented.The proposed NMLNCML system strengthens the chaotic characteristics of the system,and is applicable for image encryption.The main advantages of the proposed method are embodied in its extensive key space;high sensitivity to secret keys;great resistance to chosen-plaintext attack,statistical attack,and differential attack;and good robustness to noise and data loss.Our image cryptosystem adopts the architecture of scrambling,compression,and diffusion.First,a plain image is transformed to a sparsity coefficient matrix by discrete wavelet transform,and plaintext-related Arnold scrambling is performed on the coefficient matrix.Then,semi-tensor product(STP)compressive sensing is employed to compress and encrypt the coefficient matrix.Finally,the compressed coefficient matrix is diffused by DNA random encoding,DNA addition,and bit XOR operation.The NMLNCML system is applied to generate chaotic elements in the STP measurement matrix of compressive sensing and the pseudo-random sequence in DNA operations.An SHA-384 function is used to produce plaintext secret keys and thus makes the proposed encryption algorithm highly sensitive to the original image.Simulation results and performance analyses verify the security and effectiveness of our scheme.

考虑站点耦合关系的大型城市轨道交通网络级联失效分析

为了解析站点分布密集的大型城市轨道交通网络级联失效传播机理,提出改进的耦合映射格子模型.该模型结合大型城市轨道交通网络站点分布密集特征,量化耦合站点间客流演化及耦合站点抵抗力.为了衡量级联失效在大型城市轨道交通网络中的传播过程与结果,提出失效站点数量比与网络效率比指标.以上海市城市轨道交通网络为例,验证该模型的可行性.结果表明:当节点度高或进站客流量大的站点失效后,耦合站点间的级联失效规模是邻接站点间的约2倍,且由于耦合站点间的级联失效的影响,介数中心性大的站点失效所引起的级联失效传播速度最快.在考虑耦合站点间级联失效时,客流对大型城市轨道交通网络级联失效的作用力是拓扑结构的约9倍.研究结论可以为城市轨道交通网络的规划设计与事故管控提供科学的建议.

Discretization of Coupled Map Lattices for a Stream Cipher

Coupled map lattices （CML） have been recently used to construct ciphers. However, the complicated operations on real numbers make these CML-based ciphers difficult to analyze. This paper presents a new stream cipher with the discretized CML which operates on binary numbers. When discretizing the CML, the effective network structure is explicitly preserved to improve the confusion and diffusion. The proposed cipher can be easily analyzed using proper cryptographic techniques and has good security. The cipher has a strict lower bound on the period length of 264 and its key setup scheme achieves enough diffusion. The keystreams pass all of the NIST statistical randomness tests and have good randomness properties. In addition the cipher is resistant to the guess-and-determine attack.

Spatiotemporal quasiperiodicity transition to chaos in the one-way coupled bistability lattice system

One-way coupled optical bnstability lattice (OCBL) system for open flow is investigated. By using numerical simulations spatiotemporal quasiperiodicity is found. A rough phase diagram indicating the main spatiotemporal dynamic behavior in weakly coupled lattice is given. The transitions between spatiotemporal quasiperiodicity and chaos are observed. This result is important for the understanding of turbulence.

Experimental system of coupled map lattices

We design an optical feedback loop system consisting of a liquid-crystal spatial light modulator （SLM）, a lens, polarizers, a CCD camera, and a computer. The system images every SLM pixel onto one camera pixel. The light intensity on the camera pixel shows a nonlinear relationship with the phase shift applied by the SLM. Every pixel behaves as a nonlinear map, and we can control the interaction of pixels. Therefore, this feedback loop system can be regarded as a spatially extended system. This experimental coupled map has variable dimensions, which can be up to 512 by 512. The system can be used to study high-dimensional problems that computer simulations cannot handle.