Search Results (257)

The rapid proliferation of Internet of Things (IoT) technologies and smart grids has substantially intensified the cybersecurity challenges associated with smart energy meters (SEMs). The data collected by the plugs are transmitted via a wireless communication protocol to a smart electricity meter that acts as a local gateway. This meter centralizes the information from the various sensors, may perform data pre-processing, aggregation, or validation operations, and then forwards the information to a central server. The main contributions of this system can be categorized into two key aspects. First, the implementation of a centralized wireless local energy consumption network using the Wi-Fi protocol to coordinate smart plugs over distances of up to 20 m. Second, the real-time acquisition of power characteristics and the remote control (ON/OFF switching) of household appliances for direct appliance-level submetering purposes. Data collected by the smart meter are transmitted to a processing unit through a Semtech SX1276 LoRa transceiver communication link. The central server constitutes the processing and storage layer of the system: it receives the collected data, archives it in a dedicated database, and makes it available through analysis, visualization, and decision-support tools. This architecture enables real-time monitoring of energy consumption, anomaly detection, optimization of electrical resource use, and the development of effective energy management strategies for smart electrical grids. Although current smart meter architectures incorporate multi-layer protection mechanisms at the hardware, communication, and data levels, additional security measures are required to counter advanced cyber threats aimed at data interception and manipulation. This paper improves the security framework of smart energy meters by integrating a chaos-based encryption layer to ensure secure data transmission. Chaotic systems exhibit intrinsic properties such as sensitivity to initial conditions, pseudo-randomness, and ergodicity, which render them particularly suitable for cryptographic applications. The proposed framework employs a Lorenz-based chaotic encryption module to secure SEM-utility data exchanges. Full article

The present study is concerned with heteroclinic trajectories of a Caputo fractional-order Lorenz-type model ($0<\alpha \le 1$), a problem that has remained unresolved. Building upon previously known findings, we initially deduce two asymmetric heteroclinic connections that link the globally attracting equilibrium $E_0$, the repelling equilibrium $E_{+}$ (or $E_{-}$), and the globally attracting equilibrium $E_{-}$ (or $E_{+}$), where $E_0=(0,0,0)$ and $E_{\pm }=({\displaystyle \frac{bd\pm \sqrt{b^2{d}^2+4bc}}{2}},{\displaystyle \frac{bd\pm \sqrt{b^2{d}^2+4bc}}{2}},c+d\left({\displaystyle \frac{bd\pm \sqrt{b^2{d}^2+4bc}}{2}}\right))$. Additionally, a novel heteroclinic trajectory is identified for two separate regimes: (1) joining the repelling $E_0$ with the globally attracting $E_{+}$ ($E_{-}$, respectively), alongside a locally attracting $E_{-}$ ($E_{+}$, respectively); (2) joining the repelling $E_{-}$ ($E_{+}$, respectively) with the globally attracting $E_{+}$ ($E_{-}$, respectively), alongside a locally attracting $E_0$. All analytical claims are supported by numerical experiments. Full article

Finite-precision implementation fundamentally changes nonlinear dynamical systems by replacing continuous-state evolution with deterministic dynamics on a finite set of representable states. This study examines when that change becomes structurally important over a finite observation horizon. Quantization is treated as a resolution constraint, and an operational separation scale ${\delta }_{\mathrm{sep}}(T_0,T;\epsilon )$ is introduced to compare the implementation resolution with the attractor detail exposed by a reference trajectory. The ratio $\eta =\Delta /{\delta }_{\mathrm{sep}}$ and its associated critical bit width $b_c\left(T\right)$ are used as protocol-dependent measures for precision screening. Experiments on the Hénon map, a Lorenz system integrated by fixed-step fourth-order Runge–Kutta, and the Logistic map show strong system dependence. Hénon exhibits broad, non-monotonic finite-state reshaping across bit width, whereas Lorenz remains in a low-complexity regime over a wider low-bit range before recovering more complex recurrent behavior. Results from 100 selected occupied quantized attractor positions show that entropy alone is insufficient to characterize collapse; recurrence and transient lengths provide complementary information about orbit organization. A 21-horizon Lorenz study produces stepwise changes and a long plateau in $b_c\left(T\right)$, rather than a smooth linear scaling law. For Hénon, the largest-horizon crossing is resolved at $b_c=25.457$, corresponding to a minimum integer bit width of 26 under the declared estimator. An alternative estimator gives materially different crossing values, while the Logistic map also shows strongly non-monotonic behavior. Overall, $\eta$ and $b_c\left(T\right)$ provide useful implementation-oriented screening measures, but they are not universal thresholds or hardware guarantees. Full article

In this paper, a multi-image encryption and hiding scheme based on controllable compressive sensing and adaptive matching embedding is proposed. The highlights of this scheme include the use of adaptive data segmentation, controllable integer compressive sensing, and adaptive matching embedding. Firstly, a 512-bit master key, together with an HMAC-SHA512-based session key derivation mechanism incorporating plaintext hashes and random noise, is used to initialize the proposed Fractal–Chaos Hybrid Map—a novel chaotic system combining the Lorenz system with Mandelbrot fractal perturbations. This produces high-quality random sequences with superior randomness and a large key space. Secondly, the scheme applies DCT and adaptive data segmentation to process the plain images. The sparse data obtained from segmentation is compressed using a sensing matrix generated from random sequences, and then encoded and encrypted via random flipping. Finally, the adaptive matching embedding technique is used to embed the encrypted data into the carrier image. The proposed scheme performs excellently in both the compression encryption of plain images and the embedding of encrypted data into the carrier image. It supports the encryption and hiding of up to six plain images with an acceptable trade-off between embedding capacity and carrier image quality. A comprehensive security analysis, including statistical and differential attack evaluations, confirms the scheme’s strong resistance to various cryptographic threats while maintaining high efficiency. Full article

Cloud and quality screening removes approximately 65% of daily TROPOMI tropospheric NO₂ pixels, creating structured data gaps that coincide with meteorological conditions driving pollution extremes. Standard gap-filling methods—kriging, Random Forests and other machine learning methods—act as statistical smoothers that systematically suppress extreme concentrations and ignore the Missing Not At Random (MNAR) character of cloud-induced missingness. Here we present a physically informed framework that treats urban NO₂ as a forced nonlinear dynamical system and reconstructs missing satellite observations through geometric navigation on a shadow manifold rather than statistical interpolation. The framework integrates five components: (i) Multivariate State-Space Reconstruction (MSSR) using multiview embeddings of continuous ground-based NO₂, O₃, and ERA5 meteorology, grounded in Stark’s forced-system embedding theorem; (ii) Short-Time Regime-Conditioned Convergent Cross Mapping (ST-RC-CCM) with a spatial-mismatch negative control for falsifiable causal validation; (iii) Inverse Probability Weighting (IPW) to correct the clear-sky sampling bias; (iv) trajectory-matrix denoising via Singular Spectrum Analysis (SSA) and Robust PCA; (v) topology-inspired fidelity metrics—Manifold Overlap Ratio (MOR) and Dynamic Trend Capture (DTC)—that penalize smoothing artefacts. The physical basis for this coupling is the shared dynamical history of surface and column NO₂: tropospheric NO₂ has a photochemical lifetime of 1–4 h near urban emission sources, comparable to the boundary layer mixing timescale, ensuring that surface and column concentrations are jointly governed by the same emission–photolysis–transport attractor. The planetary boundary layer height (PBLH), solar zenith angle (SZA), and surface O₃—all included as MSSR coordinates—are the dominant physical drivers of the instantaneous surface-to-column scaling, and their joint trajectory in state space constitutes the physically grounded basis for analogue selection. The framework is validated on a synthetic forced Lorenz-96 system, then applied to five European primary cities spanning contrasting regimes (Sofia, Milano, Stuttgart, Kraków, Hamburg) plus five N1 spatial-mismatch control stations (Plovdiv, Genova, Frankfurt, Warszawa, Berlin)—ten urban-background stations across four countries—with structured ablations (A0-A4V-A4K). Across >3600 evaluations, MOR_ext distributions for EDM and non-EDM methods are non-overlapping by a factor exceeding 5× (EDM minimum 0.59 vs. non-EDM maximum 0.10; median non-EDM MOR_ext ≤ 0.05 at every city × mask combination), while EDM achieves MOR_ext up to 0.915 (Milano Po Valley). Under a fair-comparison benchmark that withholds ground-level NO₂ from Random Forest, EDM’s RMSE advantage remains robust at a median of 3.9× (RF_FULL) and increases to 4.2× (RF_METEO), confirming that the performance gap is physical rather than an information artefact. A three-level temporal validation—within-window pseudo-cloud masking, cross-year transfer (full 2022 holdout and DJF 2023/24), and a COVID-19 out-of-distribution test—demonstrates robustness beyond standard train/test splits, with CCM library-length convergence confirmed for 60/60 ablations (p < 0.001) across all ten stations. Spatial-mismatch tests confirm local dynamical specificity at all five primary–control pairs (Δρ = 0.090–0.210), with seasonal modulation driven by orographic and synoptic mechanisms. These results establish manifold-based gap filling as a dynamically informative complement to statistical approaches, particularly in topographically confined, stagnation-prone basins where preserving extreme-event geometry is essential for exposure assessment. Full article

Dissipative structures are open dynamical systems that sustain coherent macroscopic organization by continuously exchanging energy and matter with their environment and generating entropy. A recent thermodynamic analysis of the paradigmatic Malkus–Lorenz waterwheel interpreted the Lorenz system as an engine, deriving an exact formula for its thermodynamic efficiency and showing that efficiency tends to increase as the system is driven far from equilibrium while displaying sharp drops near the Hopf subcritical bifurcation to chaos. Here, we extend that single-engine framework to coupled dissipative structures. We introduce two canonical couplings—master–slave coupling (series) and symmetric diffusive coupling (parallel)—and prove two fundamental association laws allowing us to reduce the composite systems to an equivalent engine with a specified efficiency. We then apply these abstract results to coupled Lorenz waterwheels, deriving efficiency formulas consistent with the underlying power balance. We perform numerical simulations confirming that (a) series coupling induces an increase in thermodynamic efficiency, (b) parallel coupling averages the efficiency of engines and increases total energy flow, (c) synchronization is typically neutral or beneficial for efficiency except in narrow parameter regions, and (d) coupling modifies the curvature of entropy-generation trends. Our theorems suggest a mathematically rigorous and transparent route to define and compute thermodynamic efficiency for generalized flow networks, with potential application to complex systems energetics. Full article

We analyze the effect of microscopic heterogeneity on the Lorenz curve of macroscopic observables. The Lorenz curve of a response function, being a cumulative and bounded quantity; it is often a more stable function than the corresponding probability density. We show here that by doing an exponent spectrum analysis of the complementary Lorenz curve, it is possible to obtain a reflection of the underlying heterogeneity that causes the response function to depart from a power law behavior. We demonstrate this framework first by synthetic data and then by analyzing the avalanche statistics of a two dimensional, Random Field Ising Model (RFIM) at zero temperature. This method can lead to possible use in estimating the microscopic heterogeneity of a system from the analysis of an estimated Lorenz curve, particularly in socio-economic and physical contexts where the full probability distribution function is unavailable. Full article

This study presents a comparative numerical investigation of second-order and fourth-order Runge–Kutta methods for solving chaotic dynamical systems. The Lorenz, Genesio–Tesi, and Rössler systems are considered because of their nonlinear behavior and high sensitivity to initial conditions. The numerical schemes investigated include the Midpoint, Improved Euler, Ralston, and fourth-order Runge–Kutta (RK4) methods. The performance of the methods is evaluated in terms of convergence behavior, numerical accuracy, stability characteristics, and computational cost. A stability analysis of each chaotic system is carried out through equilibrium point determination and Jacobian eigenvalue analysis. Numerical simulations are implemented in MATLAB 2023 version, and comparisons are performed using different step sizes. The results indicate that all numerical methods converge as the step size decreases; however, the RK4 method consistently provides significantly smaller errors and improved stability properties compared with the second-order schemes. The findings further demonstrate that higher-order numerical integration methods provide superior performance for highly sensitive chaotic systems where accuracy and reliability are essential. Full article

Big data has generated massive amounts of multi-source data and complex data correlations, making the efficient extraction of value from these correlations a major challenge in the field. The ongoing development of complex network theory has led to the widespread application of methods that mine system correlations based on network topology. However, if correlation analysis relies solely on low-order topological features, it will overlook higher-order connectivity information at the mesoscale. First, by leveraging complex network construction algorithms, we establish a multi-layer finite-transit visual graph network and develop metrics for measuring correlation and guidance relationships by integrating high-order network information. Second, simulation experiments were conducted on the CML system, the Lorenz system, and the Rössler system, respectively. By comparing the results with traditional low-order metrics and incorporating noise interference tests, the superiority, effectiveness, and robustness of the proposed metrics in identifying correlations were validated. Finally, empirical research was conducted using data from the China Carbon Emission Trade Exchange, the EU Emissions Trading System, the Brent crude oil market, and the Chinese INE crude oil market. This analysis examined the inter-linkage characteristics between the carbon market and the crude oil market, revealing the patterns of dynamic information spillover between the two markets. Full article

Macroeconomic systems are increasingly characterized by fractal structures, entropy-generating processes, and chaotic dynamics that challenge the assumptions of traditional regression methods. The presence of self-similarity, fractal structure, and sensitivity to initial conditions suggests that macroeconomic variables evolve through complex interactions that cannot be adequately explained within an equilibrium-based method. Motivated by this perspective, this paper tested the relationships between oil prices and macroeconomic variables in the United States over the period of 1960–2024 using a suggested fractal regression approach. The analysis proceeds in two stages. In the first stage, fractal, entropy, and chaotic structures of the variables were analyzed by employing entropy measures, Lyapunov exponents, attractor diagnostics by including Lorenz and Julia structures, and tests for fractal dimension: d parameter (GPH) and d parameter (Phillips), and long range dependendeceLo’s Modified R/S, and Hurst–Mandelbrot R/S. Our results explored evidence of fractal structure, complexity, and chaotic behavior within the selected macroeconomic series by indicating the presence of nonlinear dynamics and sensitivity to initial conditions. In the second stage, a proposed chaotic–fractal-based regression model is employed to explore the transmission mechanism of oil price to economic growth, inflation, and unemployment. By directly incorporating Lyapunov and fractal-based measures into the regression method, the model captured nonlinear interactions that are overlooked by traditional methods. The results revealed that oil price shocks generate chaotic and fractal effects across macroeconomic variables and that these effects vary according to the degree of chaotic divergence embedded in the system. Overall, the results suggested the interconnected roles of fractality, entropy, and chaos in shaping macroeconomic dynamics and showed the importance of chaos- and fractal-based modeling methods for understanding the economic consequences of energy shocks and their policy implications. Full article

Maximizing the dominant Lyapunov exponent ${\lambda }_1$ of an incommensurate fractional-order chaotic system, while respecting the dynamical conditions for a strange attractor, is a non-convex, gradient-free problem on a history-dependent landscape. Existing metaheuristic studies typically use hard-cutoff penalties that distort the fitness landscape and integer-order Lyapunov estimators that can be biased for strongly fractional regimes. This paper presents a constraint-faithful optimization framework combining (i) subtractive-hinge penalties that vanish on the feasible set, (ii) a memory-consistent Grünwald–Letnikov variational Lyapunov estimator with adaptive tail-sum truncation, (iii) joint search over parameters and incommensurate orders by the Marine Predators Algorithm, and (iv) a fractional conditional Lyapunov exponent (FCLE) that recovers the integer-order limit. Applied with a fixed configuration to the fractional-order Lorenz, Ma–Chen financial, Iqbal–Wang, and Hyper–Chen systems, the framework converges to feasible attractors with enlarged Lyapunov spectra. Dissipativity is rigorously verified; all selected optima have strictly negative Lyapunov trace at the reported precision. FCLE analysis on the optimized Lorenz attractor recovers the integer-order identity $c_{min}={\lambda }_1$ under full-state coupling, and shows that single-state x-coupling raises the threshold to ≈9${\lambda }_1^{*}$. The optimized fractional-order Lorenz attractor is employed as the random-number generator of a recent chaos-based image-encryption scheme, where it yields strong statistical results across standard benchmarks. Full article

The interaction of electromagnetic waves with atmospheric aerosols plays a significant role in communication systems and multimedia information transmission. Understanding the interaction of vortex light beams with an aerosol-laden atmosphere is indispensable for establishing a framework of the environmental channel. During the interaction, different optical effects such as absorption and scattering will result in energy attenuation, and this yields the deterioration of the transmission feature of the vortex beam signal. In this study, we present a theoretical analysis of Gaussian vortex beams (GVBs) scattering by diverse aerosol (unformed carbon, dust, sulphate, silicate, soot, and nitrate) particles in the atmosphere on the basis of the well-established generalized Lorenz–Mie theory (GLMT). Combined with the lognormal distribution model for aerosol particles, the attenuation and transmission characteristics of GVBs for different aerosol particles are analyzed. The extinction efficiency $\left(Q_{ext}\right)$ factor of GVB, caused by the absorption and scattering of various aerosols, becomes smaller compared to that of a basic Gaussian beam (GB). Increasing the OAM mode index, the energy attenuation and transmission caused by aerosol absorption and scattering further decrease. Moreover, this research provides a basis to analyze the optical characteristics of the twisted beams in different atmospheric channels, such as wireless communication networks over aerosol-laden systems and material interactions. Full article

Path planning for autonomous robots is a key problem area, particularly when faced with complicated, dynamic, or uncertain environments. Even though traditional techniques (grid-based, graph-based, sampling, and optimization-based) have already been developed to solve this problem, there are notable limitations to scalability, adaptability, and responsiveness with these methods. In this paper, we explore an alternative approach based on chaotic dynamical systems, specifically chaotic attractors like those produced by the Lorenz and Rössler systems. Chaotic systems are defined by several properties that could be leveraged: non-linearity, sensitivity to initial conditions, and dense coverage of the state space are three notable properties that could be used to generate trajectories that are organized, yet ultimately unpredictable. By applying numerical integration (Runge–Kutta) directly to robot motion through MATLAB R2025b simulations, chaotic states support more effective exploration, better obstacle avoidance, and more robust navigation in dynamic or adversarial environments. The paper also examines whether chaotic path planning can be applied in multi-robot systems through state coupled robots that emerge coordinated behavior while maintaining autonomous movement. This paper is a framework for chaos theory supporting adaptable, robust navigating behaviors for purposes such as autonomous vehicles, swarm robotics, and search and rescue and surveillance applications. Full article

Complex networks have become a fundamental paradigm for modeling real-world systems. Synchronization of such networks, particularly under hyperchaotic dynamics, presents a significant control challenge due to the high-dimensional state space and multiple positive Lyapunov exponents. This paper addresses the driver node selection problem in a 4D Hyperchaotic Lorenz complex network, formulating it as a constrained binary optimization task. We evaluate a pool of advanced metaheuristics, including the quantum genetic algorithm (QGA), seahorse optimizer (SHO), and artificial bee colony (ABC), across multiple network experiments conducted over 30 independent runs to guarantee statistical validity. The performance of these solvers is rigorously benchmarked against traditional topological heuristics, a random selection baseline comprising 600 feasible configurations, and verified through Wilcoxon statistical testing. Furthermore, addressing computational sustainability, we introduce a “Green-Artificial Intelligence” architecture based on dual-tier structured query language memoization (SQL-memoization) and provide a detailed runtime comparison evaluating its efficiency. The empirical results indicate that swarm-intelligence methods such as ABC and SHO exhibit robust competitive performance in minimizing synchronization errors while the Green-AI framework consistently and drastically reduces the computation of the repetitive simulations. Full article

Agricultural supply chains operating under rural infrastructure constraints face persistent logistical inefficiencies that reduce producer income and weaken territorial sustainability. This paper assesses how collaborative and coordinated distribution architectures reshape economic performance, efficiency, and equity in dispersed networks of cocoa producers in El Carmen de Bolívar, Colombia. The unified optimization framework compares three regimes: decentralized non-collaborative individual shipments, collaborative consolidation based on distribution centers, and coordinated distribution with time-window synchronization. The findings show a reduction in average logistics costs from $0.688/kg in decentralized distribution to $0.323/kg with collaborative distribution centers, and even further to $0.282/kg in coordinated distribution, representing an overall reduction of approximately 59%. A sensitivity analysis across 64 accessibility configurations shows that the advantage of coordination increases as time rigidity increases. These structural improvements translate into a 13.97% increase in total producer utility, raising average utility from $278 to $317 per producer. In addition, the distributional assessment based on Lorenz curves and Gini coefficients indicates that inequality remains stable despite gains in welfare. These results demonstrate that spatial consolidation combined with temporal synchronization is a decisive lever for resilient and inclusive rural supply systems. Full article