Coupled Map Lattices Research Articles

Spatiotemporal complexity analysis of a discrete space-time cancer growth model with self-diffusion and cross-diffusion

We investigate spatiotemporal pattern formation in cancer growth using discrete time and space variables. We first introduce the coupled map lattices (CMLs) model and provide a dynamical analysis of its fixed points along with stability results. We then offer parameter criteria for flip, Neimark–Sacker, and Turing bifurcations. In the presence of spatial diffusion, we find that stable homogeneous solutions can experience Turing instability under certain conditions. Numerical simulations reveal a variety of spatiotemporal patterns, including patches, spirals, and numerous other regular and irregular patterns. Compared to previous literature, our discrete model captures more complex and richer nonlinear dynamical behaviors, providing new insights into the formation of complex patterns in spatially extended discrete tumor models. These findings demonstrate the model’s ability to capture complex dynamics and offer valuable insights for understanding and treating cancer growth, highlighting its potential applications in biomedical research.

Characteristics of 3D coupled map lattice and its application in pseudo-random number generator

Characteristics of 3D coupled map lattice and its application in pseudo-random number generator

Enhanced image encryption with compression using improved coupled map lattices and Fisher–Yates permutation–diffusion

Enhanced image encryption with compression using improved coupled map lattices and Fisher–Yates permutation–diffusion

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.

A privacy encryption scheme for medical images based on nonlinear dynamic coupled map lattices and protein sequence

A privacy encryption scheme for medical images based on nonlinear dynamic coupled map lattices and protein sequence

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.

Chaos synchronization of two coupled map lattice systems using safe reinforcement learning

When synchronizing two continuous typical chaotic systems, the state variables of the response system are usually bounded and satisfy the Lipschitz condition. This permits a universal synchronization method. In the synchronization of two high-dimensional discrete chaotic systems such as the coupled map lattice systems, the state variables of the response system often diverge, which makes it difficult to seek a universal synchronization method. To overcome this difficulty, bounded and hard constraints, which correspond to the concept of safety level III in reinforcement learning terms, on the state variables must be imposed, when the discrete response system is perturbed. We propose a universal method for synchronizing two discrete systems based on safe reinforcement learning (RL). In this method, the RL agent’s policy is used to reach the goal of synchronization and a safety layer added directly on top of the policy is used to satisfy safety level III. The safety layer consists of a one-step predictor for the perturbed response system and an action correction formulation. The one-step predictor, based on a next generation reservoir computing, is used to identify whether the next state of the perturbed system is within the chaotic domain, and if not, the action correction formula is activated to modify the corresponding perturbing force component to zero. In this way, the state of the perturbed system will remain in the bounded chaotic domain. We demonstrate that the proposed method succeeds in synchronization without divergence through a numerical example with two coupled map lattice systems, and the average synchronization time is 12.66 iteration steps over 1000 different initial conditions. The method works even when parameter mismatches and disturbances exist in the system. We compare the performance in both cases with and without the safety layer and find that successful synchronization is only possible in the former case, emphasizing the significance of the safety layer. The performance of the algorithm with optimal hyper-parameters obtained by Bayesian optimization is robust and stable.

Synchronization transition in space–time chaos in the presence of quenched disorder

Synchronization of two replicas of coupled map lattices for continuous maps is known to be in the multiplicative noise universality class. We study this transition in the presence of quenched disorder in coupling. The disorder is identical in both replicas. We study one-dimensional, two-dimensional, and globally coupled logistic and tent maps. We observe a clear second-order transition with new exponents. The order parameter decays as t−δ and δ depends on the map and its parameters. The asymptotic order parameter for Δ distance from a critical point grows as Δβ with β∼δ. The quenched disorder in coupling is a relevant perturbation for the replica synchronization of coupled map lattices. The critical exponents are different from those of the multiplicative noise universality class. However, it does not depend on dimensionality in the cases studied if the transition is continuous.

Spatiotemporal Patterns in a Space–Time Discrete SIRS Epidemic Model with Self- and Cross-Diffusion

In this work, a two-dimensional Coupled Map Lattice (CML) method is applied to a continuous Reaction–Diffusion (RD) SIRS epidemic model. The model involves a complex, nonlinear incidence rate and the spatially heterogeneous self- and cross-diffusion coefficients. The CML method applied here results in a space–time discrete counterpart of the model. The basic reproduction number is derived, and the local stability of the fixed points of the discrete model is established. The two typical bifurcations of codimension 1, such as the flip and the Neimark–Sacker (NS) bifurcations, are investigated by utilizing the center manifold theory and the normal form theorem. Furthermore, the codimension-2 fold–flip bifurcation about the endemic fixed point is discussed in detail. Turing instability criterion of the cross-diffusion epidemic model is established by utilizing the CML method under periodic boundary conditions. Finally, the numerical simulations clarify both the effectiveness of all theoretical findings and the effects of time step size and cross-diffusion on the spatiotemporal patterns. The main contribution of this work is the discovery of some interesting Turing and non-Turing patterns which may be induced by flip–Turing instability, NS–Turing instability or fold–flip–Turing instability. Concretely speaking, spiral patterns are observed near the flip bifurcation threshold value and ultimately evolve into an irregular defect pattern. Stripe pattern, labyrinth pattern and circular pattern are observed near the NS bifurcation threshold value. The disorderly interwoven ribbon pattern, mosaic pattern and some irregular oscillatory patterns are observed near the fold–flip bifurcation point. Our results greatly help in predicting the long-term behavior of the space–time discrete SIRS epidemic model under study.

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

Correlation between Hurst exponent and largest Lyapunov exponent on a coupled map lattice

Positive correlations have been made between the Hurst exponent and the largest Lyapunov exponent using various one-dimensional maps by other authors. We incorporate these maps into a Coupled Map Lattice (CML), and investigate whether the correlation still exists. With multiple Hurst exponents being calculated for each CML, differences between each have been shown, with the possibility of using one Hurst exponent to represent the system. Results also show that the Hurst exponent is a good indicator of chaos, and is in positive correlation with the largest Lyapunov exponent. We suggest that for a general class of CML, an increased Hurst exponent indicates an increased Lyapunov exponent 85% of the time. Given the Hurst exponent can frequently be calculated more quickly than the Lyapunov exponent we suggest it as a more time efficient measure. Through these connections, machine learning methods have been used to predict the largest Lyapunov exponent for different scenarios.

Discrete kinetic analysis of a general reaction–diffusion model constructed by Euler discretization and coupled map lattices

In this paper, we provide a framework for the Turing instability in a general two-dimensional discrete reaction–diffusion model that utilizes Euler discretization and coupled map lattices. We obtained explicit criterions for the normal forms of Neimark–Sacker bifurcation and flip bifurcation in the absence of diffusion. We derive the general conditions that govern the emergence of pure Turing instability, Neimark–Sacker–Turing instability, Flip–Turing instability, spatially homogeneous stable states, spatially homogeneous periodic oscillation states, and spatially homogeneous period-doubling oscillatory states under spatially inhomogeneous conditions. As an example, we employ a ratio-dependent predation model and verify the derived general conditions through a series of numerical simulations. Additionally, we apply the calculation of Maximum Lyapunov Exponent(MLE) to simulate and demonstrate the path from flip bifurcation to chaos.

An efficient image encryption scheme integrating chaotic keystream generator with S-box and triangular block scrambling

A novel image encryption scheme has been developed to effectively meet the growing need for image security and privacy. This scheme combines a chaotic keystream generator with S-box and triangular block scrambling to provide efficient encryption. The keystream generator consists of a two-dimensional coupled map lattice (2DCML), linear interval transformation (LIT) and an S-box. By using a 2DCML, two initial chaotic sequences are generated and used to construct an S-box. Then, a final chaotic sequence is obtained after undergoing LIT and S-box processing. The proposed algorithm applies two rounds of scrambling operations and two rounds of substitutions. During the scrambling processes, global scrambling and triangular block scrambling are combined. Diffusion operations use an S-box while incorporating a key policy linked with image content to enhance resistance against chosen-plaintext attacks. The simulation outcomes, coupled with the security analysis, substantiate the efficacy and robust encryption performance of the proposed image encryption scheme.

Pattern dynamics analysis of a time-space discrete FitzHugh-Nagumo (FHN) model based on coupled map lattices

This paper investigates the dynamics of a discrete FitzHugh-Nagumo (FHN) model with self-diffusion on two-dimensional coupled map lattices. The primary objective is to analyze the complex dynamics of neuronal systems in a discrete setting. Through the application of central manifold and normal form analysis, it has been demonstrated that the system is capable of undergoing Neimark-Sacker and flip bifurcations even in the absence of diffusion. Additionally, when influenced by diffusion, the system can manifest pure Turing instability, Neimark-Sacker-Turing instability, and Flip-Turing instability. In the numerical simulation section, the path from bifurcation to chaos is explored by calculating the maximum Lyapunov exponent and drawing the bifurcation diagram. The interconversion between various Turing instabilities is simulated by varying the values of the time step and the self-diffusion coefficient. This study contributes to a deeper understanding of the complexity of neural network systems.

Monostable pulsating traveling waves in discrete periodic media with delay

The purpose of this article is to investigate various qualitative properties of pulsating traveling waves for a delayed lattice dynamical system with global interaction in periodic habitat. Under some appropriate assumptions, we first establish a Harnack type of inequality for its wave profile system. Then, we show that all wave profiles remain strictly increasing in the propagation process. Based on the Harnack’s inequality and monotonicity result, the other effort of the article is devoted to the exponential decay of the non-critical pulsating traveling waves towards the unstable steady state. Finally, we obtain the uniqueness of all non-critical pulsating traveling waves.

Coupling Effect and Chain Evolution of Urban Rail Transit Emergencies

Emergency events such as fire, flood and COVID-19 occurred in urban rail transit (URT) usually triggered chain effect and evolved into huge disaster. This kind of chain with complexity and uncertainty evolution brought great challenges to the safety management of the system. Thus, the coupling effects of emergencies and then its relationship with the chain evolution is necessary to analyze emphatically. A Graph Evaluation and Review Technique Simulation (GERTS) evolution network is firstly constructed to describe the coupling effect and chain evolution of emergencies. Then, considering the internal and external influencing factors of the emergency chain, a dynamic evolution model of the emergency chain based on Coupled Map Lattice (CML) is proposed. This paper takes fire chain of URT as an example to simulate the evolution process of emergency chain, and analyze the impact of different coupling effects and various influencing factors on the evolution of emergency chain. The results of numerical simulation show that the AND-coupling can significantly inhibit the evolution of emergency events, while the OR-coupling and CO-coupling can expand the impact scope of emergency events. In addition, the evolution speed of emergency events can be controlled by increasing the coupling action time and improving the URT repair ability. When an emergency event occurs, the analysis of coupling effect and the accompanied chain evolution will help managers to make scientific judgment on the development trend of the emergency events and make targeted emergency defense measures.

Cascading Reliability Assessment of International Railway Freight Network Based on Coupled Map Lattices: A Case Study of China Railway Express

Cascading Reliability Assessment of International Railway Freight Network Based on Coupled Map Lattices: A Case Study of China Railway Express

Time series synchronization in cross-recurrence networks: uncovering a homomorphic law across diverse complex systems

Exploring the synchronicity between time series, especially the similar patterns during extreme events, has been a focal point of research in academia. This is due to the fact that such special dependence occurring between pairs of time series often plays a crucial role in triggering emergent behaviors in the underlying systems and is closely related to systemic risks. In this paper, we investigate the relationship between the synchronicity of time series and the corresponding topological properties of the cross-recurrence network (CRN). We discover a positive linear relationship between the probability of pairwise time series event synchronicity and the corresponding CRN’s clustering coefficient. We first provide theoretical proof, then demonstrate this relationship through simulation experiments by coupled map lattices. Finally, we empirically analyze three instances from financial systems, Earth’s ecological systems, and human interactive behavioral systems to validate that this regularity is a homomorphic law in different complex systems. The discovered regularity holds significant potential for applications in monitoring financial system risks, extreme weather events, and more.

Invariant measures for first order nonlocal lattice dynamical systems with delays

Invariant measures for first order nonlocal lattice dynamical systems with delays