Coupled Map Lattices Research Articles

Secure Real-Time Chaotic Partial Encryption of Entropy-Coded Multimedia Information for Mobile Devices: Smartphones

Smartphones penetration-rate continues expanding, from 44% in 2017 up to 59% expected increase in 2022 as reported by Strategy Analytics. At present, smartphones dominate the global mobile traffic, which in turn is dominated by video communications. For mobile systems with limited power capabilities, the processing of real-time multimedia information with affixed security represents a real challenge. In this work, we propose a high-performance encryption scheme capable of running on low-power smartphones without holding back video coding operation. We are aimed at destroying the meaning of the entropy coded bitstream by inserting random bit errors to induce error propagation and impede natural self-resynchronization process. The scheme consists of three main process: 1) A new integer <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">chaos-based Coupled-Map Lattice</i> -CML for creating secure pseudo-random trajectories; 2) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Random bit flipping</i> of the bitstream based on a Dynamic Reference Point (DRP) not exposed to attackers; and 3) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Random selection</i> of CML byte-trajectories for both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DRP</i> and bit flipping processes for increased security. Implementation of the scheme on smartphones with different CPU-power capabilities shows <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">excellent performance</i> to handle high-bandwidth real-time video smoothly (one-to-one and group calls). The scheme provides high scalable security with encrypted data volume fluctuating between 0.7%-3% of the total compressed data (video and still images).

A plain-text independent color image encryption system with multi-thread permutation and multi-channel diffusion

In this paper, we present a novel multi-threaded parallel permutation and channel-combined diffusion for image encryption which is independent of plain text. In our proposed method, the coupled map lattice is used to generate the key sequences for multi-thread permutation and diffusion. Then intra- and inter-thread permutations are achieved using multi-threading in combination with the tent mapping. For the subsequent diffusion, this paper introduces a method based on channel-combined diffusing which simultaneously diffuses three channels. Experimental results indicate a high encryption performance with the capability of effectively resisting the known plain text and differential attacks. Our proposed method also has a lower computational complexity which enables its applicability in practical scenarios.

Machine learning applied to pattern characterization in spatially extended dynamical systems

This new tool, in the form of Machine Learning (ML), has proven to be very useful in several areas of physics, due to its strong versatility, its ability to obtain patterns in very complex systems. In this work we explore techniques from Machine Learning (ML) to characterize spatio-temporal patterns in complex dynamical systems. These techniques are applied in coupled map lattices, for which the relevant parameters are the nonlinearity and coupling strength. As a training phase of our ML, we show several samples with the dynamic characteristics of each known space–time profile, such as frozen random pattern, pattern selection, chaotic defects, intermittency and fully developed space–time chaos, for example. After the training phase, we apply our algorithm to different values of non-linearity and coupling, where given the dynamic characteristics, for each pair of parameters, we can accurately identify the regions where each of these profiles is formed.

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.

Chimera state in coupled map lattice of matrices

In recent years, a lot of research has focused on understanding the behavior of when synchronous and asynchronous phases occur, that is, the existence of chimera states in various networks. Chimera states have wide-range applications in many disciplines including biology, chemistry, physics, or engineering.&#x0D; The object of research in this paper is a coupled map lattice of matrices when each node is described by an iterative map of matrices of order two. A regular topology network of iterative maps of matrices was formed by replacing the scalar iterative map with the iterative map of matrices in each node. The coupled map of matrices is special in a way where we can observe the effect of divergence. This effect can be observed when the matrix of initial conditions is a nilpotent matrix.&#x0D; Also, the evolution of the derived network is investigated. It is found that the network of the supplementary variable $\mu$ can evolve into three different modes: the quiet state, the state of divergence, and the formation of divergence chimeras. The space of parameters of node coupling including coupling strength $\varepsilon$ and coupling range $r$ is also analyzed in this study. Image entropy is applied in order to identify chimera state parameter zones.

Pixel-level and bit-level image encryption method based on Logistic-Chebyshev dynamic coupled map lattices

This paper proposes two new chaotic systems. One is one-dimensional Logistic-Chebyshev map (1DLCM) and the other is Logistic-Chebyshev dynamic coupled map lattices (LCDCML). LCDCML uses 1DLCM as the dynamic coupling coefficient, which meet the cryptographic characteristics and are suitable for studying image encryption. Based on these two systems, a pixel-level and bit-level image encryption algorithm is proposed. The specific encryption algorithm first generates the chaotic sequence by the LCDCML system. The scrambling part adopts pixel-level and bit-level scrambling combined with chaotic sequences. The pixel-level scrambling uses dynamic row and column index scrambling. The bit-level scrambling uses dynamic circular traversal and dynamic cyclic shifts. Then, the image is diffused by a special formula combined with chaotic sequences. Finally, this encryption scheme can also be extended to color images. Experimental simulation and performance analysis show that the encryption algorithm has higher security.

Random attractor and exponentially stability for the second order nonautonomous retarded lattice systems with multiplicative white noise

In this paper, we first present some conditions for the existence of a random attractor of continuous non-autonomous random dynamical systems (cocycle) and locally coupled stochastic retarded lattice dynamical systems in a space of continuous functions from finite closed interval into a product space of finite weighted spaces of infinite sequences. Then we consider the existence, singleton and exponentially stability of the random attractor for the second order non-autonomous retarded lattice systems with multiplicative white noise.

Coupled hypergraph maps and chaotic cluster synchronization

Coupled map lattices (CMLs) are prototypical dynamical systems on networks/graphs. They exhibit complex patterns generated via the interplay of diffusive/Laplacian coupling and nonlinear reactions modelled by a single iterated map at each node; the maps are often taken as unimodal, e.g., logistic or tent maps. In this letter, we propose a class of higher-order coupled dynamical systems involving the hypergraph Laplacian, which we call coupled hypergraph maps (CHMs). By combining linearized (in-)stability analysis of synchronized states, hypergraph spectral theory, and numerical methods, we detect robust regions of chaotic cluster synchronization occurring in parameter space upon varying coupling strength and the main bifurcation parameter of the unimodal map. Furthermore, we find key differences between Laplacian and hypergraph Laplacian coupling and detect various other classes of periodic and quasi-periodic patterns. The results show the high complexity of coupled graph maps and indicate that they might be an excellent universal model class to understand the similarities and differences between dynamics on classical graphs and dynamics on hypergraphs.

Initial perturbation matters: Implications of geometry-dependent universal Kardar-Parisi-Zhang statistics for spatiotemporal chaos.

Infinitesimal perturbations in various systems showing spatiotemporal chaos (STC) evolve following the power laws of the Kardar-Parisi-Zhang (KPZ) universality class. While universal properties beyond the power-law exponents, such as distributions and correlations and their geometry dependence, are established for random growth and related KPZ systems, the validity of these findings to deterministic chaotic perturbations is unknown. Here, we fill this gap between stochastic KPZ systems and deterministic STC perturbations by conducting extensive simulations of a prototypical STC system, namely, the logistic coupled map lattice. We show that the perturbation interfaces, defined by the logarithm of the modulus of the perturbation vector components, exhibit the universal, geometry-dependent statistical laws of the KPZ class despite the deterministic nature of STC. We demonstrate that KPZ statistics for three established geometries arise for different initial profiles of the perturbation, namely, point (local), uniform, and "pseudo-stationary" initial perturbations, the last being the statistically stationary state of KPZ interfaces given independently of the Lyapunov vector. This geometry dependence lasts until the KPZ correlation length becomes comparable to the system size. Thereafter, perturbation vectors converge to the unique Lyapunov vector, showing characteristic meandering, coalescence, and annihilation of borders of piece-wise regions that remain different from the Lyapunov vector. Our work implies that the KPZ universality for stochastic systems generally characterizes deterministic STC perturbations, providing new insights for STC, such as the universal dependence on initial perturbation and beyond.

Unstable dynamics of solitary traveling waves in a lattice with long-range interactions

In this work we revisit the existence, stability and dynamics of traveling solitary waves in the context of lattice dynamical systems. We consider a nonlinear lattice of an α-Fermi-Pasta–Ulam type with the additional feature of all-to-all harmonic long-range interactions whose strength decays exponentially with distance. The competition between the nonlinear nearest-neighbor terms and the longer-range linear terms yields two parameter regimes where the dependence of the energy H of the traveling waves on their velocity c is non-monotonic and multivalued, respectively. We examine both cases, and identify the exact (up to a prescribed numerical tolerance) traveling waves. To investigate the stability of the obtained solutions, we compute their Floquet multipliers, thinking of the traveling wave problem as a periodic one modulo shifts. We show that in the general case when the relationship between H and c is not necessarily single-valued, a stability threshold corresponds to H′(s)=0, where s is the parameter along the energy–velocity curve. Perturbing the unstable solutions along the corresponding eigenvectors, we identify two different scenarios of the dynamics of their transition to stable branches. In the first case, the perturbed wave slows down after expelling a dispersive wave. The second scenario involves an increase in the velocity of the perturbed wave accompanied by the formation of a slower small-amplitude traveling solitary wave.

Attractors for multi-valued lattice dynamical systems with nonlinear diffusion terms

This paper is devoted to the long-term behavior of nonautonomous random lattice dynamical systems with nonlinear diffusion terms. The nonlinear drift and diffusion terms are not expected to be Lipschitz continuous but satisfy the continuity and growth conditions. We first prove the existence of solutions, and establish the existence of a multi-valued nonautonomous cocycle. We then show the existence and uniqueness of pullback attractors parameterized by sample parameters. Finally, we establish the measurability of this pullback attractor by the method based on the weak upper semicontinuity of the solutions.

Amplitude death in coupled replicator map lattice: Averting migration dilemma.

Populations composed of a collection of subpopulations (demes) with random migration between them are quite common occurrences. The emergence and sustenance of cooperation in such a population is a highly researched topic in the evolutionary game theory. If the individuals in every deme are considered to be either cooperators or defectors, the migration dilemma can be envisaged: The cooperators would not want to migrate to a defector-rich deme as they fear of facing exploitation; but without migration, cooperation cannot be established throughout the network of demes. With a view to studying the aforementioned scenario, in this paper, we set up a theoretical model consisting of a coupled map lattice of replicator maps based on two-player-two-strategy games. The replicator map considered is capable of showing a variety of evolutionary outcomes, like convergent (fixed point) outcomes and nonconvergent (periodic and chaotic) outcomes. Furthermore, this coupled network of the replicator maps undergoes the phenomenon of amplitude death leading to nonoscillatory stable synchronized states. We specifically explore the effect of (i) the nature of coupling that models migration between the maps, (ii) the heterogenous demes (in the sense that not all the demes have the same game being played by the individuals), (iii) the degree of the network, and (iv) the cost associated with the migration. In the course of investigation, we are intrigued by the effectiveness of the random migration in sustaining a uniform cooperator fraction across a population irrespective of the details of the replicator dynamics and the interaction among the demes.

A spatiotemporal chaotic system based on pseudo-random coupled map lattices and elementary cellular automata

The coupled map lattices (CML) is a spatiotemporal chaotic system with complex dynamic behavior. In this paper, we propose a spatiotemporal chaotic system with a novel pseudo-random coupling method based on elementary cellular automata (ECA), and introduce different perturbations into lattices in each iteration according to ECA. We investigate the spatiotemporal dynamic properties and chaotic behaviors of the proposed system such as bifurcation diagrams, Kolmogorov Sinai entropy, and uniformity. Moreover, the randomness of sequences generated by the proposed system and the correlation between any two lattices are discussed. Theory analyses and simulations indicate that the new system has better performance in complexity, ergodic and unpredictability than other CML systems such as adjacent CML and nonlinear CML based on fractional order logistic equation, etc. Furthermore, the correlation coefficient between any two lattices in the proposed system is significantly lower than other systems, and another advantage of the proposed system is utilizing the output of ECA to perturb the chaotic system which can effectively alleviate the dynamical degradation in digital system. The excellent performance of the proposed system demonstrates that it has great potential for crypto-system.

Testing reliability of the spatial Hurst exponent method for detecting a change point

AbstractThe reliability of using abrupt changes in the spatial Hurst exponent for identifying temporal points of abrupt change in climate dynamics is explored. If a spatio-temporal dynamical system undergoes an abrupt change at a particular time, the time series of spatial Hurst exponent obtained from the data of any variable of the system should also show an abrupt change at that time. As expected, spatial Hurst exponents for each of the two variables of a model spatio-temporal system – a globally coupled map lattice based on the Burgers' chaotic map – showed abrupt change at the same time that a parameter of the system was changed. This method was applied for the identification of change points in climate dynamics using the NCEP/NCAR data on air temperature, pressure and relative humidity variables. Different abrupt change points in spatial Hurst exponents were detected for the data of these different variables. That suggests, for a dynamical system, change point detected using the two-dimensional detrended fluctuation analysis method on a single variable alone is insufficient to comment about the abrupt change in the system dynamics and should be based on multiple variables of the dynamical system.

Transition to Fully or Partially Arrested State in Coupled Logistic Maps on a Ladder

Layered structures are an object of interest for theoretical and experimental reasons. In this work, we study coupled map lattice on a ladder. The ladder consists of two one-dimensional chains coupled at every point. We study linearly and nonlinearly coupled logistic maps in this system and study transition to nonzero persistence, in particular. We coarse-grain the variable value by assigning spin [Formula: see text] ([Formula: see text]) to sites that have value greater (less) than the fixed point and compute the number of sites that have not changed their spin values at all even times till the given time [Formula: see text]. The fraction of such sites at a given time [Formula: see text] is known as persistence. In our system, we observe a power-law of persistence at the critical value of coupling. This transition is also accompanied by long-range antiferromagnetic ordering for nonlinear coupling and long-range ferromagnetic ordering for linear coupling. The number of domain walls decay as [Formula: see text] at the critical point in both cases. The persistence exponent is 0.375 for a nonlinear case with two layers which is an exponent for the voter model on the ladder as well as for the Ising model at zero temperature or voter model in 1D. For linear coupling, we obtain a smaller persistence exponent.

Efficient watermarking algorithm for digital audio/speech signal

Ensuring conflicting requirements such as imperceptibility, payload capacity, and robustness, becomes a great challenge for a robust audio/speech watermarking algorithm. To achieve this, this paper proposes a blind and robust audio/speech watermarking algorithm that combines the discrete Tchebichef moment transform (DTMT), the chaotic system of the mixed linear–nonlinear coupled map lattices (MLNCML), and discrete wavelet transform (DWT). The watermark is encrypted by the MLNCML system, and then it is embedded in the norm of the Tchebichef moments of the low frequency components. DTMT and MLNCML are used to achieve high robustness, high payload capacity, and high security, while DWT is used to achieve a satisfactory level of imperceptibility. In addition, the adopted strategy has a blind nature, where no original audio/speech is needed in watermark extraction. Compared to other existing audio/speech watermarking algorithms, the proposed algorithm gives better results in terms of robustness and payload capacity while keeping the embedding effect non-perceptible and undetectable.

Fitness landscapes for coupled map lattices.

Our goal is to match some dynamical aspects of biological systems with that of networks of coupled logistic maps. With these networks we generate sequences of iterates, convert them to symbol sequences by coarse-graining, and count the number of times combinations of symbols occur. Comparison of this with the number of times these combinations occur in experimental data-a sequence of interbeat intervals for example-is a measure of the fitness of each network to describe the target data. The most fit networks provide a cartoon that suggests a decomposition of the experimental data into a component that may be produced by a simple dynamical subsystem, and a residual component, the result of detailed, particular characteristics of the system that generated the target data. In the space of all network parameters, each point corresponds to a particular network. We construct a fitness landscape when we assign a fitness to each point. Because the parameters are distributed continuously over their ranges, and because fitnesses are estimated numerically, any plot of the landscape involves a finite sample of parameter values. We'll investigate how the local landscape geometry changes when the array of sample parameters is refined, and use the landscape geometry to explore complex relations between local fitness maxima.

A model to predict bottlenecks over time in a remanufacturing system under uncertainty.

Bottleneck shifting prediction has been widely applied to the remanufacturing system for throughput improvement, and it would directly influence the general presentation of the remanufacturing system. However, predicting dynamic bottlenecks of remanufacturing systems is complicated due to the disturbed environment (e.g. various processing time and uncertain processing routes). This paper built a metamorphosis CNT conjunct with coupled map lattice (CML) algorithm to predict the bottleneck shifting phenomenon in remanufacturing for the first time. The CNT was applied to the articulation of remanufacturing process, while the CML algorithm was devoted to calculating the dynamic indicator of the bottleneck. We took the value-added connecting rod as the research object to illustrate the availability of the proposed method. As validated by Arena simulation, the approach presented in this paper put forward is feasible to make an accurate prediction for shifting bottlenecks in a remanufacturing system.

On the forward dynamical behaviour of nonautonomous lattice dynamical systems

In this article, we study the forward dynamical behaviour of nonautonomous lattice systems. We first construct a family of sets in the arbitrary small neighbourhood of a global attractor of the skew-product flow generated by a general nonautonomous lattice system, which is forward invariant and uniformly forward attracts any bounded subset of the phase space. Moreover, under some suitable conditions, we further construct a family of sets such that it uniformly forward exponentially attracts bounded subsets of the phase space. As an application, we study the discrete Gray–Scott model in detail and illustrate how to apply our abstract results to some concrete lattice system.

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.