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.

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

In the paper, we study effects of scale-free （SF） topology on dynamical synchronization and control in coupled map lattices （CIVIL）. Our strategy is to apply three feedback control methods, including constant feedback and two types of time-delayed feedback, to a small fraction of network nodes to reach desired synchronous state. Two controlled bifurcation diagrams verses feedback strength are obtained respectively. It is found that the value of critical feedback strength γc for the first time-delayed feedback control is increased linearly as e is increased linearly. The GML with SF loses synchronization and intermittency occurs if γ 〉 γc. Numerical examples are presented to demonstrate all results.

A Cryptographic Scheme Based on Spatiotemporal Chaos of Coupled Map Lattices

We propose a cryptographic scheme based on spatiotemporal chaos of coupled map lattices （CIVIL） ,which is based on one-time pad. The structure of the cryptosystem determines that the progress in decryption implies the progress in exploring the dynamical behavior of spatiotemporal chaos in CML. A part of the initial condition of CML is used as a secret key, and the recovery of the secret key by exhaustive search is impossible due to the sensitivity to the initial condition in spatiotemporal chaos system. Specially the software implementation of the scheme is easy.

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

We present a self-synchronizing stream encryption scheme based on one-dimensional coupled map lattices which is introduced as a model with the essential features of spatiotemporal chaos, and of great complexity and diffusion capability of the little disturbance in the initial condition. To evaluate the scheme, a series of statistical tests are employed, and the results show good random-look nature of the ciphertext. Furthermore, we apply our algorithm to encrypt a grey-scale image to show the key sensitivity.

Periodic Windows in Weakly Coupled Map Lattices

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 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.

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.

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.

Control of cascading failures in coupled map lattices based on adaptive predictive pinning control

An adaptive predictive pinning control is proposed to suppress the cascade in coupled map lattices (CMLs).Two monitoring strategies are applied:(1) A specific fraction of nodes with the highest degree or betweenness are chosen to constitute the set of monitored nodes;(2) During the cascade,an adaptive pinning control is implemented,in which only the nodes in the monitored set whose current state is normal but whose predictive state is abnormal,are pinned with the predictive controller.Simulations show that for the scale-free (SF) CML the degree-based monitoring strategy is advantageous over the betweenness-based strategy,while for the small-world (SW) CML the situation is the opposite.With the adaptive predictive pinning control,the fewer local controllers can effectively suppress the cascade throughout the whole network.

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.

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.

A New Approach to Synchronization Analysis of Linearly Coupled Map Lattices

In this paper, a new approach to analyze synchronization of linearly coupled map lattices （LCMLs） is presented. A reference vector x（t） is introduced as the projection of the trajectory of the coupled system on the synchronization manifold. The stability analysis of the synchronization manifold can be regarded as investigating the difference between the trajectory and the projection. By this method, some criteria are given for both local and global synchronization. These criteria indicate that the left and right eigenvectors corresponding to the eigenvalue ＂0＂ of the coupling matrix play key roles in the stability of synchronization manifold for the coupled system. Moreover, it is revealed that the stability of synchronization manifold for the coupled system is different from the stability for dynamical system in usual sense. That is, the solution of the coupled system does not converge to a certain knowable s（t） satisfying s（tT1） = f（s（t）） but to the reference vector on the synchronization manifold, which in fact is a certain weighted average of each x^i（t） for i=1,……, m, but not a solution s（t） satisfying s（t ＋ 1）=f（s（t））.

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.

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.

Chimera states in Gaussian coupled map lattices

We study chimera states in one-dimensional and two-dimensional Gaussian coupled map lattices through simulations and experiments. Similar to the case of global coupling oscillators, individual lattices can be regarded as being controlled by a common mean field. A space-dependent order pa- rameter is derived from a self-consistency condition in order to represent the collective state.

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.