Coupled Map Lattice Model Research Articles

A novel plaintext-related image encryption and compression method based on a new coupled map lattices model

In this paper, we propose a new Sine-Logistic Map Coupled Map Lattices (SLMCML) model, which exhibits enhanced chaotic characteristics and more suitable for image encryption compared with the classical coupled map lattices. Based on the SLMCML system, we propose an image encryption and compression method. To improve the plaintext sensitivity of image cryptosystem, we propose a novel plaintext-related internal keys generation method, which can obviously improve the plaintext sensitivity of initial values of SLMCML system, thus improve the plaintext sensitivity of whole process of compression and encryption. Our proposed image encryption scheme contains several steps. Initially, the discrete wavelet transform (DWT) is utilized to convert original image into coefficient matrix. Then a plaintext relation method is constructed, which generate internal keys as initial values of SLMCML system. Next the coefficient matrix is permutated by permutation sequences generated by SLMCML system to cyclic shift for making the energy evenly distributed. Next the coefficient matrix is done sparse processing. The compressed sensing is employed to compress coefficient matrix. Subsequently, the compressive image is permutated with spiral traversal and twice zigzag transform. Finally, the permutated image is diffused with column diffusion to generate cipher image. Through some common security analyses, our proposed image encryption scheme has good security performance and excellent image recovery quality.

Nonlinear dynamics and pattern formation in a space–time discrete diffusive intraguild predation model

In this paper, the spatiotemporal dynamics and pattern formation of a space–time discrete intraguild predation model with self-diffusion are investigated. The model is obtained by applying a coupled map lattice (CML) method. First, using linear stability analysis, the existence and stability conditions for fixed points are determined. Second, using the center manifold theorem and the bifurcation theory, the occurrence of flip, Neimark-Sacker, and Turing bifurcations are discussed. It is shown that the patterns obtained are results of Turing, flip, and Neimark-Sacker instabilities. Numerical simulations are performed to verify the theoretical analysis and to reveal complex and rich dynamics of the model, such as times series, maximal Lyapunov exponent, bifurcation diagrams, and phase portraits. Interesting patterns like spiral pattern, polygonal pattern, and the combinations of patterns of spiral waves and stripes are formed. The CML model’s results help to understand how a spatially extended, discrete intraguild predation model forms complex patterns. Notably, the continuous reaction–diffusion counterpart of the model under study is incapable of experiencing Turing instability.

An novel dynamic compressed sensing method for image encryption based on a new coupled map lattices model

An novel dynamic compressed sensing method for image encryption based on a new coupled map lattices model

An improved coupled map lattice model and its application in image encryption

An improved coupled map lattice model and its application in image encryption

Understanding the Level of Turbulence by Asymmetric Distributions: A Motivation for Measurements in Space Plasmas

In this article, on the basis of the Langevin equation applied to velocity fluctuations, we numerically model the partial variance of increments, which is a useful tool to measure time and spatial correlations in space plasmas. We consider a coupled map lattice model to relate the spatial scale of fluctuations, k, to some macro parameters of the systems, such as the Reynolds number, R λ , the κ parameter of Kappa distributions, and a skewness parameter, δ. To do so, we compute the velocity probability density function (pdf) for each spatial scale and different values of Reynolds number in the simulations. We fit the pdf with a Skew–Kappa distribution, and we obtain a numerical relationship between the level of turbulence of the plasma and the skewness of obtained distributions, namely, . We expect the results exposed in this paper to be useful as a tool to characterize the turbulence in the context of space plasma and other environments.

A novel image encryption algorithm based on coupled map lattices model

A novel image encryption algorithm based on coupled map lattices model

Quantifying bus route service disruptions under interdependent cascading failures of a multimodal public transit system based on an improved coupled map lattice model

The coupled map lattice (CML) model can present rich spatiotemporal dynamic behaviors of complex systems, e.g., it has been observed to have good adaptability in the cascading failure modeling of subway networks (SNs). However, most studies rarely considered an interdependency between an SN and a bus network (BN), which reveals an open problem concerning the CML model's adaptability to a multimodal public transit system (MPTS). This paper develops an improved CML model to simulate interdependent cascading failures of an MPTS and quantify bus route service disruptions for amplifying severe consequences of failures. Remarkably, an interdependency integrating operational and nonlinear geographical interdependencies is proposed to modify the node state evolutionary function and model cascading failures across layers. Moreover, an estimation method for the node initial state is proposed to accommodate the initial value-sensitive dependence due to a logistic chaotic map involved in the evolutionary function. Finally, a case is simulated to verify the model's adaptability and enlighten operation management. Results indicate that (i) the neglect of interdependency causes an overestimation of the severity of cascading failures of an SN while a severe underestimation of those of a BN; (ii) the management and engineering measures to adjust transfers both have a phase transition point on the controllability of cascading failures, and the latter exhibits more a direct and comprehensive effect.

Reconstruction of complex network from time series data based on graph attention network and Gumbel Softmax

It is a challenging practical problem to infer the network structure from measurable time series data. Recently, with the rapid development of graph deep learning, Zhang et al. [Appl. Netw. Sci. 4, 110 (2019)] applied graph neural network to the field of network reconstruction and proposed Gumbel Graph Network. In this paper, a graph deep learning network reconstruction method based on graph attention network and Gumbel Softmax (GAT-GS) is proposed, which can realize high accuracy network reconstruction and node state prediction of discrete and continuous systems. The GAT-GS model is designed based on the dynamic equation of nodes. It consists of two parts: a network structure learner to reconstruct a more real rather than functionally connected networks, based on Gumbel Softmax sampling to generate network structures; and a node state learner using graph attention networks to learn the state evolution of nodes, with the introduction of Laplacian matrix and adjacency matrix for better adaptation to diffusion coupling and unidirectional coupling systems. This model is trained to dynamically adjust the network adjacency matrix and attention coefficients to obtain the network structure and predict the node state. Experimental results show that the GAT-GS model has high reconstruction accuracy, strong robustness and high universality. It can be applied to various kinds of dynamic systems, including Coupled Map Lattice model and Lorenz system, can deal with time series data from regular to complete chaos, can reconstruct various kinds of complex networks, including regular network, Barabási–Albert network and Watts–Strogatz small world network, and it can also reconstruct networks from small scale to large scale with higher computational efficiency.

Coupled-Map-Lattices-Based Vulnerability Assessment of UAV Network in Interference Scenarios

On the modern information battlefield, UAV have been widely used due to the advantages of no casualties and good maneuverability. However, during the UAV swarm combat, the UAV network will be interfered by the enemy, which will damage some key UAV nodes or communication links and affect the connectivity of the entire network, thus leading to the fact that the entire network becomes more vulnerable. Therefore, it is necessary to study the network vulnerability of UAV networks in interference scenarios. In this paper, a coupled map lattice (CML) model which is a dynamic system with discrete time, discrete space, and continuous state variables is proposed to assess the vulnerability of UAV networks. The CML model integrates multiple topological indicators such as node degree, node betweenness, and node clustering coefficient, and reflects the node state change of the UAV network in the interference scenario from the topological point of view. When changing the strategy of interfering UAV nodes in different interfering scenarios, the relative network efficiency and failure proportion are used as indicators to study the change of network vulnerability. The studies show that precisely interfering important UAV nodes in a network can cause more damage to the UAV network. We also discover that as the intensity of external interference increases, the entire network will become increasingly vulnerable and the vulnerability of the network will also have different manifestations under different interfering strategies.

Observation and a simple model of plumose pattern on fracture surfaces of drying pastes

Plumose pattern often appears on the fracture surface of drying pastes. We show a few experimental results of the crack propagation in the drying pastes. We find that the crack propagation sometimes exhibits jump motions. We have also performed an experiment of the crack propagation in a tilted container where the crack propagates from the deeper to shallower sides. This experimental result suggests the importance of the movement of water content. We propose a simple coupled map lattice model. In the numerical simulation, a plumose-like pattern appears owing to the instability of the flat surface of the fracture. The numerical simulation reproduces the jump motions in the crack propagation. We have performed another experiment where a vertical streak pattern appears when the crack propagates downward by cutting into the top surface of the drying paste.

Critical parameters of the synchronisation's stability for coupled maps in regular graphs

Coupled Map Lattice (CML) models are particularly suitable to study spatially extended behaviours, such as wave-like patterns, spatio-temporal chaos, and synchronisation. Complete synchronisation in CMLs emerges when all maps have their state variables with equal magnitude, forming a spatially-uniform pattern that evolves in time. Here, we derive critical values for the parameters – coupling strength, maximum Lyapunov exponent, and link density – that control the synchronisation-manifold's linear stability of diffusively-coupled, identical, chaotic maps in generic regular graphs (i.e., graphs with uniform node degrees) and class-specific cyclic graphs (i.e., periodic lattices with cyclical node permutation symmetries). Our derivations are based on the Laplacian matrix eigenvalues, where we give closed-form expressions for the smallest non-zero eigenvalue and largest eigenvalue of regular graphs and show that these graphs can be classified into two sets according to a topological condition (derived from the stability analysis). We also make derivations for two classes of cyclic graph: k-cycles (i.e., regular lattices of even degree k, which can be embedded in Tk tori) and k-Möbius ladders, which we introduce here to generalise the Möbius ladder of degree k = 3. Our results highlight differences in the synchronisation manifold's stability of these graphs – even for identical node degrees – in the finite size and infinite size limit.

Vulnerability assessment of freeway network considering the probabilities and consequences from a perspective based on network cascade failure.

Freeway networks are vulnerable to natural disasters and man-made disruptions. The closure of one or more toll stations of the network often causes a sharp decrease in freeway performance. Therefore, measuring the probability and consequences of vulnerability to identify critical parts in the network is crucial for road emergency management. Most existing techniques only measure the consequences of node closure and rarely consider the probability of node closure owing to the lack of an extensive historical database; moreover, they ignore highways outside the study area, which can lead to errors in topological analysis and traffic distribution. Furthermore, the negative effects produced by the operation of freeway tunnels in vulnerability assessment have been neglected. In this study, a framework for freeway vulnerability assessment that considers both the probability and consequences of vulnerability is proposed, based on the perspective of network cascade failure analysis. The cascade failure analysis is conducted using an improved coupled map lattice model, developed by considering the negative effects of tunnels and optimizing the rules of local traffic redistribution. The perturbation threshold and propagation time step of network cascade failure are captured to reflect the probabilities and consequences of vulnerability. A nodal vulnerability index is established based on risk assessment, and a hierarchical clustering method is used to identify the vulnerability classification of critical nodes. The freeway network of Fuzhou in China is utilized to demonstrate the effectiveness of the proposed approach. Specifically, the toll stations in the study area are classified into five clusters of vulnerability: extremely high, high, medium, low, and extremely low. Approximately 31% of the toll stations were classified as the high or extremely high cluster, and three extremely vulnerable freeway sections requiring different precautions were identified. The proposed network vulnerability analysis method provides a new perspective to examine the vulnerability of freeway networks.

A New Full Chaos Coupled Mapping Lattice and Its Application in Privacy Image Encryption

Since chaotic cryptography has a long-term problem of dynamic degradation, this paper presents proof that chaotic systems resist dynamic degradation through theoretical analysis. Based on this proof, a novel one-dimensional two-parameter with a wide-range system mixed coupled map lattice model (TWMCML) is given. The evaluation of TWMCML shows that the system has the characteristics of strong chaos, high sensitivity, broader parameter ranges and wider chaos range, which helps to enhance the security of chaotic sequences. Based on the excellent performance of TWMCML, it is applied to the newly proposed encryption algorithm. The algorithm realizes double protection of private images under the premise of ensuring efficiency and safety. First, the important information of the image is extracted by edge detection technology. Then the important area is scrambled by the three-dimensional bit-level coupled XOR method. Finally, the global image is more fully confused by the dynamic index diffusion formula. The simulation experiment verified the effectiveness of the algorithm for grayscale and color images. Security tests show that the application of TWMCML makes the encryption algorithm have a better ability to overcome conventional attacks.

Modeling network vulnerability of urban rail transit under cascading failures: A Coupled Map Lattices approach

In terms of urban rail transit network vulnerability, most studies have focused on the changes of network topology and functional characteristics under disruptive events while ignoring the impacts of cascading failures on network performance. In this study, an improved Coupled Map Lattices model is proposed to address the evolution process of cascading failures on rail transit network. Particularly, the model quantifies important factors of cascading failures integrating quantitative failure spreading mode, anti-risk ability of stations, and perturbation index. The rail transit network vulnerability is then modeled addressing numbers of failed stations, degree of affected passengers, and loss of passenger travel time as a result of cascading failures. The methodology is applied to the metro network of Shanghai, China. Results show that the propagation of network cascading failure depends on the station's anti-risk ability, geographical location, and type of adjacent stations. Stations located in the urban center area are more susceptible to failures of adjacent stations. Furthermore, higher affected passenger volume and station coupling strength would lead to more serious and rapid spreading of failures, and thus more vulnerable of the metro system. However, the anti-risk ability of stations could effectively resist the spread of failures in the early stage, and stations with higher topology redundancy demonstrate stronger anti-risk ability.

Performance of the 2D Coupled Map Lattice Model and Its Application in Image Encryption

The two‐dimensional coupled map lattice (2D CML) model has been extensively employed as the basis component for designing various schemes in the cryptography system due to its complicated chaotic dynamic behavior. In this study, we analyze the chaotic characteristics of the 2D CML model, such as the Lyapunov exponent (LE), synchronization stability, bifurcation, and ergodicity. We then show that the chaotic sequences generated by the 2D CML model are random according to the NIST testing. Furthermore, we propose an image encryption scheme based on the 2D CML model and Singular Value Decomposition (SVD). In our scheme, the SVD method is used to reduce the image storage, and the Red, Green, and Blue channels of a color image will be encrypted through confusion and diffusion. The simulation results, as well as the results of the comparison with other schemes, demonstrate that our scheme possesses outstanding statistics, excellent encryption performance, and high security. It has great potential for ensuring the security of digital images in real applications.

Bifurcation Analysis of a 2-D Logistic Coupled Map Lattice Model

Bifurcation Analysis of a 2-D Logistic Coupled Map Lattice Model

Cascading Failure Analysis on Shanghai Metro Networks: An Improved Coupled Map Lattices Model Based on Graph Attention Networks.

Analysis of the robustness and vulnerability of metro networks has great implications for public transport planning and emergency management, particularly considering passengers’ dynamic behaviors. This paper presents an improved coupled map lattices (CMLs) model based on graph attention networks (GAT) to study the cascading failure process of metro networks. The proposed model is applied to the Shanghai metro network using the automated fare collection (AFC) data, and the passengers’ dynamic behaviors are simulated by GAT. The quantitative cascading failure analysis shows that Shanghai metro network is robust to random attacks, but fragile to intentional attacks. Moreover, there is an approximately normal distribution between instant cascading failure speed and time step and the perturbation in a station which leads to steady state is approximately a constant. The result shows that a station surrounded by other densely distributed stations can trigger cascading failure faster and the cascading failure triggered by low-level accidents will spread in a short time and disappear quickly. This study provides an effective reference for dynamic safety evaluation and emergency management in metro networks.

Analysis of cascading failures of interdependent networks based on time-delay coupled map lattices model

The robustness of coupled network under cascading failure has attracted a lot of attention. In real word, the networks don’t exist in isolation, and the interdependent network is an important network model. In the process of fault propagation, there is usually delay, and a node may have multiple interdependent links. A cascading failure model based on coupled map latices for small word interdependent network is built in this paper. The research shows that when the external perturbation 3.7<R<4.0, the cascading failure ranges of high-degree and random strategy in interdependent network are close, and the different time-delay can induce different range of cascading failure in interdependent network. The thresholds of the external perturbation are common under different time-delay when the whole interdependent network is failed. The time-delay also can prolong the failure spreading time during which measures can be taken to suppress cascading failures. The research can provide a reference for building high-robust transport interdependent network.

Urban Rail Transit System Network Reliability Analysis Based on a Coupled Map Lattice Model

During the last twenty years, the complex network modeling approach has been introduced to assess the reliability of rail transit networks, in which the dynamic performance involving passenger flows have attracted more attentions during operation stages recently. This paper proposes the passenger-flow-weighted network reliability evaluation indexes, to assess the impact of passenger flows on network reliability. The reliability performances of the rail transit network and passenger-flow-weighted one are analyzed from the perspective of a complex network. The actual passenger flow weight of urban transit network nodes was obtained from the Shanghai Metro public transportation card data, which were used to assess the reliability of the passenger-flow-weighted network. Furthermore, the dynamic model of the Shanghai urban rail transit network was constructed based on the coupled map lattice (CML) model. Then, the processes of cascading failure caused by network nodes under different destructive situations were simulated, to measure the changes of passenger-flow-weighted network reliability during the processes. The results indicate that when the scale of network damage attains 50%, the reliability of the passenger-flow-weighted network approaches zero. Consequently, taking countermeasures during the initial stage of network cascading may effectively prevent the disturbances from spreading in the network. The results of the paper could provide guidelines for operation management, as well as identify the unreliable stations within passenger-flow-weighted networks.

A Novel Compressive Image Encryption with an Improved 2D Coupled Map Lattice Model

The digital image, as the critical component of information transmission and storage, has been widely used in the fields of big data, cloud and frog computing, Internet of things, and so on. Due to large amounts of private information in the digital image, the image protection is fairly essential, and the designing of the encryption image scheme has become a hot issue in recent years. In this paper, to resolve the shortcoming that the probability density distribution (PDD) of the chaotic sequences generated in the original two-dimensional coupled map lattice (2D CML) model is uneven, we firstly proposed an improved 2D CML model according to adding the offsets for each node after every iteration of the original model, which possesses much better chaotic performance than the original one, and also its chaotic sequences become uniform. Based on the improved 2D CML model, we designed a compressive image encryption scheme. Under the condition of different keys, the uniform chaotic sequences generated by the improved 2D CML model are utilized for compressing, confusing, and diffusing, respectively. Meanwhile, the message authentication code (MAC) is employed for guaranteeing that the encryption image be integration. Finally, theoretical analysis and simulation tests both demonstrate that the proposed image encryption scheme owns outstanding statistical, well encryption performance, and high security. It has great potential for ensuring the digital image security in application.