Coupled Map Lattices Research Articles

Snaking bifurcations of localized patterns on ring lattices

Abstract We study the structure of stationary patterns in bistable lattice dynamical systems posed on rings with a symmetric coupling structure in the regime of small coupling strength. We show that sparse coupling (for instance, nearest-neighbour or next-nearest-neighbour coupling) and all-to-all coupling lead to significantly different solution branches. In particular, sparse coupling leads to snaking branches with many saddle-node bifurcations, while all-to-all coupling leads to branches with six saddle nodes, regardless of the size of the number of nodes in the graph.

Beyond Statistical Analysis in Chaos-Based CSPRNG Design

The design of cryptographically secure pseudorandom number generator (CSPRNG) producing unpredictable pseudorandom sequences robustly and credibly has been a nontrivial task. Almost all the chaos-based CSPRNG design approaches invariably depend only on statistical analysis. Such schemes designed to be secure are being proven to be predictable and insecure day by day. This paper proposes a design and instantiation approach to chaos-based CSPRNG using proven generic constructions of modern cryptography. The proposed design approach with proper instantiation of such generic constructions eventually results in providing best of both worlds that is the provable security guarantees of modern cryptography and passing of necessary statistical tests as that of chaos-based schemes. Also, we introduce a new coupled map lattice based on logistic-sine map for the construction of CSPRNG. The proposed pseudorandom number generator is proven using rigorous security analysis as that of modern cryptography and tested using the standard statistical testing suites. It is observed that the generated sequences pass all stringent statistical tests such as NIST, Dieharder, ENT, and TestU01 randomness test suites.

Cascading failures in coupled map lattices with sustained attack

Many realistic networked systems may face sustained attack over a sequence of time. In this paper, we propose a cascading failure model in coupled map lattices (CMLs) with sustained attack, where a number of crucial nodes will be attacked one by one at each time step. The effects of four attacking strategies: high-degree strategy (HDS), high-clustering coefficient strategy, high-closeness strategy and high-betweenness strategy are compared. This shows that the performance of HDS is better than that of other attacking strategies when the value of the outside attack is small. The effectiveness of HDS on Watts–Strogatz (WS) small-world networks and two real-world networks is extensively investigated. The results indicate that increasing the value of the rewiring probability of WS networks can make the network more robust to resist sustained attack. The sparser the network structure is, the faster the diffusion velocity of cascading failures is. A smaller coupling strength in CMLs can restrain the diffusion velocity of cascades. We also extend our CML-based model with sustained attack from one node strategy (ONS) to two nodes strategy (TNS) and compare the effect of ONS and TNS with different values of the outside attack. It is found that ONS outperforms TNS for small values of the outside attack, but TNS would be a better choice when the outside attack and the time step are all large. Our work will provide new insights into the problem of protecting complex networks against cascading failures with respect to malicious attack.

Spatiotemporal chaos in multiple coupled mapping lattices with multi-dynamic coupling coefficient and its application in color image encryption

• A new spatiotemporal chaos (SMDMCML) was proposed and its application in color images. • Adopted two-way independent diffusion method is used to forward diffusion and backward independent diffusion. • The strategy of simultaneously shuffling and diffusion was adopted to realize non-linear diffusion. • The proposed scheme only needs one round of encryption to get good effects. • The superior performance of the proposed algorithm was proved by experiments in color images. This paper proposes a new sine-multi dynamic multiple coupling mapping lattice (SMDMCML). Through comprehensive analysis, the SMDMCML system enhances the behavior of spatiotemporal dynamics and is more stable on the whole. Moreover, the states of lattices in SMDMCML are more chaotic than the coupled map lattice (CML) or even the multiple coupled mapping lattices (MCML) models. Therefore, a new two-way independent diffusion in color image encryption algorithm is proposed based on SMDMCML. Through simulation experiments analysis, R, G, and B components have lower correlation and higher sensitivity. This further proves that SMDMCML system has good chaotic performance and conforms to characteristics of cryptography .

Blind and safety-enhanced dual watermarking algorithm with chaotic system encryption based on RHFM and DWT-DCT

This study proposes a novel blind watermarking algorithm based on radial harmonic Fourier moments (RHFMs) as well as discrete wavelet transform and discrete cosine transform (DWT-DCT) to achieve copyright protection. A non-adjacent coupled map lattice chaotic system was used to improve the safety in the watermark embedding process. First, a zero-watermark was obtained by performing DCT on the original image. Meanwhile, the direction information of the origin was calculated and embedded in the RHFM domain. During normal watermark embedding, the image-embedded direction information was transformed by a one-level DWT and the low-frequency sub-band was divided into 8×8 non-overlapping blocks. Each block was transformed by DCT, and two low-frequency coefficients were selected to embed the encrypted watermark. Experimental results demonstrated that the proposed algorithm is robust against rotation and other attacks. The analysis also showed that the proposed algorithm satisfies the invisibility of watermarking algorithms and has good security performance.

Self-organized criticality in cumulus clouds.

The shape of clouds has proven to be essential for classifying them. Our analysis of images from fair weather cumulus clouds reveals that, in addition to turbulence, they are driven by self-organized criticality. Our observations yield exponents that support the fact the clouds, when projected to two dimensions, exhibit conformal symmetry compatible with c=-2 conformal field theory. By using a combination of the Navier-Stokes equation, diffusion equations, and a coupled map lattice, we successfully simulated cloud formation, and obtained the same exponents.

Comparative study of positive feedbacks on linear and nonlinear coupled logistic maps

This is an extended work of the authors on coupled logistic maps with delayed linear, or non-linear nearest neighbor coupling. Here we investigate the effect of positive feedback in the coupled map lattices with update rules on (i) the phase diagrams showing non-zero persistence in the μ-ε parameter space, and (ii) on power law exponents of decay of persistence. We find that while feedback is increased the increased non-zero persistence regions in the phase diagram has no noticeable effect on the power law exponents. We also find that the role played by time lag in the absence of feedback, discussed in our previous work, remains intact even with the introduction of feedback. We offer an extensive comparison of without feedback and with feedback plots.

Vulnerability assessments of weighted urban rail transit networks with integrated coupled map lattices

This paper proposes an integrated coupled map lattices (ICML) to assess the node states and study the vulnerability of weighted urban rail transit networks (URTNs) subjected to the external disturbance R. Meanwhile, the passenger flow is refined as the passenger in-flow and out-flow of the station, and a new passenger flow redistribution rule is proposed to discuss the cascading failures of URTNs. Moreover, three parameters are adopted to analyze the vulnerability characteristics of URTNs subjected to cascading failures and Nanjing metro network is taken as the example to verify the feasibility and effectiveness of the presented model. The results show that there is a linear relationship between the node betweenness and edge betweenness, and URTNs are very vulnerable subjected to malicious attacks and become more and more vulnerable with the increase of the external disturbance. Furthermore, we find that the largest degree node-based attack (LDA) is more likely to result in cascading failures and the highest betweenness node-based attack (HBA) can cause the most damage to URTNs subjected malicious attacks. We also discover that the external disturbance R=2 is the critical threshold to smash the Nanjing metro network subjected to the largest degree node-based attack, and R=2.3 is the critical threshold to crush Nanjing metro network subjected to the highest betweenness node-based attack and the largest strength node-based attack.

A Novel Intermittent Jumping Coupled Map Lattice Based on Multiple Chaotic Maps

Coupled Map Lattice (CML) usually serves as a pseudo-random number generator for encrypting digital images. Based on our analysis, the existing CML-based systems still suffer from problems like limited parameter space and local chaotic behavior. In this paper, we propose a novel intermittent jumping CML system based on multiple chaotic maps. The intermittent jumping mechanism seeks to incorporate the multi-chaos, and to dynamically switch coupling states and coupling relations, varying with spatiotemporal indices. Extensive numerical simulations and comparative studies demonstrate that, compared with the existing CML-based systems, the proposed system has a larger parameter space, better chaotic behavior, and comparable computational complexity. These results highlight the potential of our proposal for deployment into an image cryptosystem.

Pattern dynamics in the Belousov-Zhabotinsky coupled map lattice

The Dynamics of the Belousov-Zhabotinsky (BZ) coupled map lattice (CML) was studied as a model of spatiotemporal pattern. The systematical change of coupling strength and bifurcation parameter led to the shifts in the patterns of the BZ CML. The phase diagram of the BZ CML was different from that of the logistic CML. The phases, such as fully developed turbulence, pattern competition intermittency and pattern selection observed in the logistic CML, appeared in the BZ CML. However, the dynamics of the BZ CML were more sensitive to the coupling strength than those of the logistic CML. In addition, the periodic oscillation phase was observed as small a number of patterns without the domain of chaotic motion. Furthermore, we discussed the difference between the BZ and the logistic CML on the basis of intermittency of chaos.

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.

A privacy image encryption algorithm based on piecewise coupled map lattice with multi dynamic coupling coefficient

This paper proposes a new tent-multi dynamic piecewise coupled mapping lattice (TMDPCML). Through the comprehensive analysis of the performance test results, TMDPCML system increases the correlation dynamics of spatiotemporal behavior and improves the efficiency of energy diffusion between lattices. Moreover, TMDPCML system has larger parameter space, better chaos and outstanding cryptographic characteristics. Therefore, this paper proposes a privacy image encryption algorithm combined with TMDPCML system. The application of TMDPCML system in private images encryption further proves that TMDPCML system has good chaotic behavior and meets the requirements of cryptography.

A new image encryption algorithm based on\xa0the OF-LSTMS and chaotic sequences

In this paper, a novel image encryption algorithm based on the Once Forward Long Short Term Memory Structure (OF-LSTMS) and the Two-Dimensional Coupled Map Lattice (2DCML) fractional-order chaotic system is proposed. The original image is divided into several image blocks, each of which is input into the OF-LSTMS as a pixel sub-sequence. According to the chaotic sequences generated by the 2DCML fractional-order chaotic system, the parameters of the input gate, output gate and memory unit of the OF-LSTMS are initialized, and the pixel positions are changed at the same time of changing the pixel values, achieving the synchronization of permutation and diffusion operations, which greatly improves the efficiency of image encryption and reduces the time consumption. In addition the 2DCML fractional-order chaotic system has better chaotic ergodicity and the values of chaotic sequences are larger than the traditional chaotic system. Therefore, it is very suitable to image encryption. Many simulation results show that the proposed scheme has higher security and efficiency comparing with previous schemes.

A secure image encryption scheme based on genetic mutation and MLNCML chaotic system

This paper presents a novel encryption scheme based on genetic operations and Mixed Linear-Nonlinear Coupled Logistic Map Lattice (MLNCML) spatiotemporal chaotic system. The initial values of the MLNCML system are related to the plain-image. Therefore, this scheme is sensitive to the plaintext and keys. For the simplicity and efficiency of the encryption process, expanded XOR (eXOR) operation and genetic operations are applied in the scheme. Spatiotemporal chaotic system can resist dynamical degradation and periodic phenomena, which offers good randomness for encryption. Moreover, the eXOR operation in this paper can effectively avoid the chosen-plaintext attack of traditional XOR operation. The DNA mutation and crossover operations are controlled by chaotic sequences, which overcome man-in-the-middle attack in the traditional DNA addition and subtraction operation. The experimental results indicate that the proposed scheme has good security to resist common attacks.

A modified salp swarm algorithm (SSA) combined with a chaotic coupled map lattices (CML) approach for the secured encryption and compression of medical images during data transmission

Medical image data analysis is a significant data in medical systems to analyze patient's health record. The biomedical image processing techniques and modernization of image devices are enhancing the medical image data. The main advantages of medical imaging data are (i) the medical imaging data are transmitted in the secure network in safe from the hackers (ii) medical imaging data can be shared quickly and easily between health care providers and departments. The chaotic system based different encryption algorithms using researches is analyzed. There are numerous issues in transmission of image such as weak security, small key space and high computational time. In this manuscript, a combined coupled map lattice (CML) with modified salp swarm algorithm is proposed. This algorithm compresses and encrypts the image using coupled map lattice (CML). This CML initially generates the number of encrypted images in modified SSA population. After the initialization, the modified SSA with whale optimization algorithm (WOA) is applied to reduce the computational time and maximize entropy in image cipher. To enhance the security of medical image is encrypted as a cipher image and transmits over the network. The experimental outcomes demonstrate that the proposed technique is more efficient to encrypt the medical image and has capability to resist the different distinct attacks.

Dynamic Robustness Analysis of a Two-Layer Rail Transit Network Model

Robustness is one of the most important performance criteria for any rail transit network (RTN), because it helps us enhance the efficiency of RTN. Several studies have addressed the issue of RTN robustness primarily from the perspectives of given rail network structures or static distributions of passenger flow. An open problem that remains in fully understanding RTN robustness is how to take the spatio-temporal characteristics of passenger travel into consideration, since the dynamic passenger flow in an RTN can readily trigger unexpected cascading failures. This paper addresses this problem as follows: (1) we propose a two-layer rail transit network (TL-RTN) model that captures the interactions between a rail network and its corresponding dynamic passenger flow network, and then (2) we conduct the cascading failure analysis of the TL-RTN model based on an extended coupled map lattice (CML). Specifically, our proposed model takes the strategy of passenger flow redistribution and the passenger flow capacity of each station into account to simulate the human mobility behaviors and to estimate the maximum passenger flow appeal in each station, respectively. Based on the smart card data of RTN passengers in Shanghai, our experiments show that the TL-RTN robustness is related to both external perturbations and failure modes. Moreover, during the peak hours on weekdays, due to the large passenger flow, a small perturbation will trigger a 20% cascading failure of a network. Having ranked the cascade size caused by the stations, we find that this phenomenon is determined by both the hub nodes and their neighbors.

Application of Coupled Map Lattice as an Alternative to Classical Finite Difference Method for Solving the Convection-Diffusion Boundary Value Problem

This paper presents a mathematical model for a piston flow reactor based on the material balance law using partial differential equations. A more general, nondimensional variant of the model is also derived. The finite difference method and coupled map lattice are used to create numerical algorithms to simulate spatio-temporal behavior in the studied system. The paper also includes a stability analysis of the proposed algorithms and results of numerous numerical simulations, done in order to compare both methods and to visualize the spatio-temporal behavior of the reactor and the effects of different model parameters. Discussion of the obtained results and comparison of both algorithms is also provided.

Exact asymptotic behavior of pulsating traveling waves for a periodic monostable lattice dynamical system

This paper is concerned with the pulsating traveling waves of a periodic lattice dynamical system with monostable nonlinearity. We first establish the exponential upper and lower bounds of the pulsating wave profiles at minus infinity. Then we prove the uniqueness result and derive the asymptotic behavior of all non-critical monostable pulsating traveling waves. This might be the first time to obtain the exact asymptotic behavior of the pulsating traveling waves for periodic discrete systems towards the unstable steady state.

Chaotic Simulator for Bilevel Optimization of Virtual Machine Placements in Cloud Computing

The drastic increase in engineering system complexity has spurred the development of highly efficient optimization techniques. Many real-world optimization problems have been identified as bilevel/multilevel as well as multiobjective. The primary aim of this work is to present a framework to tackle the bilevel virtual machine (VM) placement problem in cloud systems. This is done using the coupled map lattice (CML) approach in conjunction with the Stackelberg game theory and weighted-sum frameworks. The VM placement problem was modified from the original multiobjective (MO) problem to an MO bilevel formulation to make it more realistic albeit more complicated. Additionally comparative analysis on the performance of the CML approach was carried out against the particle swarm optimization method. A new bilevel metric called the cascaded hypervolume indicator is introduced and applied to measure the dominance of the solutions produced by both methods. Detailed analysis on the computational results is presented.