Search Results (978)

To capture bus passenger flow fluctuations and address the problems of slow convergence and high error in machine learning parameter optimization, this paper develops an improved Whale Optimization Algorithm (IWOA) integrated with a Bidirectional Gated Recurrent Unit (BiGRU). First, a Logistic–Tent chaotic mapping is introduced to generate a diverse and high-quality initial population. Second, a hybrid mechanism combining elite opposition-based learning and Cauchy mutation enhances population diversity and reduces premature convergence. Third, a cosine-based adaptive convergence factor and inertia weight strategy improve the balance between global exploration and local exploitation. Based on the correlation analysis between bus passenger flow and weather condition data in Harbin, and combined with the fluctuation characteristics of bus passenger flow, the data were divided into windows with a 7-day weekly cycle and processed by fuzzy information granulation to obtain three groups of fuzzy granulated window data, namely LOW, R, and UP, representing the fluctuation trend and spatial characteristics of bus passenger flow. The IWOA was employed to optimize and solve parameters such as the hidden layer weights and bias vectors of the BiGRU, thereby constructing a bus passenger flow fluctuation trend and spatial prediction model based on FIG-IWOA-BiGRU. Simulation experiments with 21 benchmark functions and real bus data verified its effectiveness. Results show that IWOA significantly improves optimization accuracy and convergence speed. For bus passenger flow forecasting, the average MAE, RMSE, and MAPE of LOW, R, and UP data are 2915, 3075, and 8.1%, representing improvements over existing classical models. The findings provide reliable decision support for bus scheduling and passenger travel planning. Full article

In dynamic and information-rich contexts, systems must be capable of making instantaneous, context-aware decisions. Such scenarios require optimization methods that are both fast and flexible. This paper introduces an innovative hardware-based intelligent optimization framework, deployed on FPGAs, designed to support autonomous decisions in real-time systems. In contrast to conventional methods based on a single chaotic map, our scheme brings together six separate chaotic generators in simultaneous operation, orchestrated by an adaptive voting system based on past results. The system, in conjunction with the Secretary Bird Optimization Algorithm (SBOA), constantly adjusts its optimization approach according to the changing profile of the objective function. This delivers first-rate, timely solutions with improved convergence, resistance to local minima, and a high degree of adaptability to a variety of decision-making contexts. Simulations carried out on reference standards and engineering problems have demonstrated the scalability, responsiveness, and efficiency of the proposed model. These characteristics make it particularly suitable for use in embedded intelligence applications in sectors such as intelligent production, robotics, and IoT-based infrastructures. The suggested solution was tested using post-synthesis simulations on Vivado 2022.2 and experimented on three concrete engineering challenges: welded beam design, pressure equipment design, and tension/compression spring refinement. In each situation, the adaptive selection process dynamically determined the most suitable chaotic map, such as the logistics map for the Welded Beam Design Problem (WBDP) and the Tent map for the Pressure Vessel Design Problem (PVDP). This led to ideal results that exceed both conventional static methods and recent references in the literature. The post-synthesis results on the Nexys 4 DDR (Artix-7 XC7A100T, Digilent Inc., Pullman, WA, USA) show that the initial Q16.16 implementation exceeded the device resources (128% LUTs and 100% DSPs), whereas the optimized Q4.8 representation achieved feasible deployment with 80% LUT utilization, 72% DSP usage, and 3% FF occupancy. This adjustment reduced resource consumption by more than 25% while maintaining sufficient computational accuracy. Full article

The increasing adoption of digital technologies, robotic systems, and IoT applications in sectors such as medicine, agriculture, and industry drives a surge in data generation and necessitates secure and efficient encryption. For resource-constrained systems, lightweight yet robust cryptographic algorithms are critical. This study addresses the security demands of IoRT systems by proposing an enhanced chaos-based encryption method. The approach integrates the lightweight structure of NIST-standardized Ascon-AEAD128 with the randomness of the Zaslavsky map. Ascon-AEAD128 is widely used on many hardware platforms; therefore, it must robustly resist both passive and active attacks. To overcome these challenges and enhance Ascon’s security, we integrate into Ascon the keys and nonces generated by the Zaslavsky chaotic map, which is deterministic, nonperiodic, and highly sensitive to initial conditions and parameter variations.This integration yields a chaos-based Ascon variant with a higher encryption security relative to the standard Ascon. In addition, we introduce exploratory variants that inject non-repeating chaotic values into the initialization vectors (IVs), the round constants (RCs), and the linear diffusion constants (LCs), while preserving the core permutation. Real-time tests are conducted using Raspberry Pi 3B devices and ROS 2–based IoRT robots. The algorithm’s performance is evaluated over 100 encryption runs on 12 grayscale/color images and variable-length text transmitted via MQTT. Statistical and differential analyses—including histogram, entropy, correlation, chi-square, NPCR, UACI, MSE, MAE, PSNR, and NIST SP 800-22 randomness tests—assess the encryption strength. The results indicate that the proposed method delivers consistent improvements in randomness and uniformity over standard Ascon-AEAD128, while remaining comparable to state-of-the-art chaotic encryption schemes across standard security metrics. These findings suggest that the algorithm is a promising option for resource-constrained IoRT applications. Full article

This paper presents a detailed study of the $(3+1)$-dimensional Zakharov–Kuznetsov–Burgers equation to investigate shock-wave phenomena in dusty plasmas with quantum effects. The model provides significant physical insight into nonlinear dispersive and dissipative structures arising in charged-dust–ion environments, corresponding to both laboratory and astrophysical plasmas. We then perform a qualitative, numerically assisted dynamical analysis using bifurcation diagrams, multistability checks, return maps, Poincaré sections, and phase portraits. For both the unperturbed and a perturbed system, we identify chaotic, quasi-periodic, and periodic regimes from these numerical diagnostics; accordingly, our dynamical conclusions are qualitative. We also examine frequency-response and time-delay sensitivity, providing a qualitative classification of nonlinear behavior across a broad parameter range. After establishing the global dynamical picture, traveling-wave solutions are obtained using the Paul–Painlevé approach. These solutions represent shock and solitary structures in the plasma system, thereby bridging the analytical and dynamical perspectives. The significance of this study lies in combining a detailed dynamical framework with exact traveling-wave solutions, allowing a deeper understanding of nonlinear shock dynamics in quantum dusty plasmas. These results not only advance theoretical plasma modeling but also hold potential applications in plasma-based devices, wave propagation in optical fibers, and astrophysical plasma environments. Full article

In the pursuit of sustainable development, optimizing water resources management while maintaining ecological balance is crucial. This study introduces a Chaos-enhanced Harris Hawks Optimizer (CEHHO) aimed at optimizing natural flow patterns in cascade reservoirs. First, an ecological scheduling model considering ensuring guaranteed output is established based on the similarity of ecological flows. Subsequently, the CEHHO algorithm is proposed, which uses tilted skew chaos mapping for population initialization, improving the quality of the initial population. In the exploration phase, an adaptive strategy enhances the efficiency of group search algorithms, enabling effective navigation of the complex solution space. A random difference mutation strategy, combined with the Q-learning algorithm, mitigates premature convergence and maintains algorithmic diversity. Comparative analysis with the existing technology under different typical hydrological frequency shows that the search accuracy and convergence efficiency of the proposed method are significantly improved. Under the guaranteed output limit of 1000 MW, the proposed method enhances the optimal, median, mean, and worst values by 293.92, 493.23, 422.14, and 381.15, respectively, compared to the HHO. Furthermore, the results of the multi-purpose guaranteed output scenario highlight the superior detection and exploitation capabilities of this algorithm. These findings highlight the great potential of the proposed method for practical engineering applications, providing a reliable tool for optimizing water resources management while maintaining ecological balance. Full article

In recent years, fractional-order controllers have garnered increasing attention due to their enhanced flexibility and superior dynamic performance in control system design. Among them, the fractional-order Proportional–Integral–Derivative (FOPID) controller offers two additional tunable parameters, $\lambda$ and $\mu$, expanding the design space and allowing for finer performance tuning. However, the increased parameter dimensionality poses significant challenges for optimisation. To address this, the present study investigates the application of FOPID controllers to a two-wheeled self-balancing robot (TWSBR), with controller parameters optimised using intelligent algorithms. A novel Multi-Strategy Improved Beluga Whale Optimization (MSBWO) algorithm is proposed, integrating chaotic mapping, elite pooling, adaptive Lévy flight, and a golden sine search mechanism to enhance global convergence and local search capability. Comparative experiments are conducted using several widely known algorithms to evaluate performance. Results demonstrate that the FOPID controller optimised via the proposed MSBWO algorithm significantly outperforms both traditional PID and FOPID controllers tuned by other optimisation strategies, achieving faster convergence, reduced overshoot, and improved stability. Full article

Emergency departments worldwide face challenges in managing fluctuating patient demand, which is often inadequately addressed by traditional forecasting methods due to the inherent nonlinearities of data. The purpose of this study is to propose a short-term prediction model for daily attendance in a private emergency healthcare unit in southern Brazil. The study employed seven years of historical data to compare the performance of ARIMA, Artificial Neural Networks (ANNs), and the chaotic logistic map model to forecast next-day arrivals in two specialties, general clinic and pediatric. The errors for the general practitioner and the pediatricians of the ARIMA, ANN, and logistic map models were, respectively, [0.31%, 2.54%, 2.17%] and [32.72%, 10.11%, 7.85%], measured by MAPE (mean absolute percentage error). The logistic map ranked second and first place, respectively, providing acceptable results in both cases. The main innovation is the successful application of a chaotic model, specifically the logistic map, exclusively for one-day prediction variables in the management of health and medical services. In particular, for the pediatrician, a most irregular time series, the logistic map provided the better outcome. For professionals, the study offers an accurate tool for optimizing the allocation of human and material resources and supporting daily strategic decisions. For scholars, it opens research avenues, addressing a gap in the body of knowledge on chaotic models that have not yet been extensively explored in healthcare service demand one-day forecasting. Full article

Optimization dispatch with flexible load participation in new power systems significantly enhances renewable energy accommodation, though the potential of flexible loads remains underexploited. To improve renewable utilization efficiency, promote wind/PV consumption and reduce carbon emissions, this paper establishes a low-carbon economic optimization dispatch model for active distribution networks incorporating flexible loads and tiered carbon trading. First, a hybrid SSA (Sparrow Search Algorithm)–CNN-LSTM model is adopted for accurate renewable generation forecasting. Meanwhile, multi-type flexible loads are categorized into shiftable, transferable and reducible loads based on response characteristics, with tiered carbon trading mechanism introduced to achieve low-carbon operation through price incentives that guide load-side participation while avoiding privacy leakage from direct control. Considering the non-convex nonlinear characteristics of the dispatch model, an improved Beluga Whale Optimization (BWO) algorithm is developed. To address the diminished solution diversity and precision in conventional BWO evolution, Tent chaotic mapping is introduced to resolve initial parameter sensitivity. Finally, modified IEEE-33 bus system simulations demonstrate the method’s validity and feasibility. Full article

Classifying study objects into groups is facilitated by fuzzy classifiers based on a set of rules and membership functions. Typically, the characteristics of the study objects are used to establish the criteria for classification. This work arises from the need to design fuzzy classifiers in contexts where real data is scarce or highly random, proposing a design based on statistics and chaotic maps that simplifies the design process. This study introduces the development of a fuzzy classifier, assuming that three features of the population to be classified are random variables. A Mamdani fuzzy inference system and three pseudorandom number generators based on one-dimensional chaotic maps are utilized to achieve this. The logistic, Bernoulli, and tent chaotic maps are implemented to emulate the random features of the target population, and their statistical distribution functions serve as input to the fuzzy inference system. Four experimental tests were conducted to demonstrate the functionality of the proposed classifier. The results show that it is possible to achieve a symmetric and robust classification through simple adjustments to membership functions, without the need for supervised training, which represents a significant methodological contribution, especially because this indicates that designers with minimal experience can build effective classifiers in just a few steps. Real applications of the proposed design may focus on the classification of biomedical signals (sEMG), network traffic, and personalized medical assistance systems, where data exhibits high variability and randomness. Full article

Addressing the problems of wind power’s anti-peak regulation characteristics, increasing system peak regulation difficulty, and wind power uncertainty causing frequency deviation leading to power imbalance, this paper considers the peak shaving and valley filling function and frequency regulation characteristics of energy storage, establishing a day-ahead and intraday coordinated two-stage optimization scheduling model for research. Stage 1 establishes a deterministic wind power prediction model based on time series Autoregressive Integrated Moving Average (ARIMA), adopts dynamic peak-valley identification method to divide energy storage operation periods, designs energy storage peak regulation working interval and reserves frequency regulation capacity, and establishes a day-ahead 24 h optimization model with minimum cost as the objective to determine the basic output of each power source and the charging and discharging plan of energy storage participating in peak regulation. Stage 2 still takes the minimum cost as the objective, based on the output of each power source determined in Stage 1, adopts Monte Carlo scenario generation and improved scenario reduction technology to model wind power uncertainty. On one hand, it considers how energy storage improves wind power system inertia support to ensure the initial rate of change of frequency meets requirements. On the other hand, considering energy storage reserve capacity responding to frequency deviation, it introduces dynamic power flow theory, where wind, thermal, load, and storage resources share unbalanced power proportionally based on their frequency characteristic coefficients, establishing an intraday real-time scheduling scheme that satisfies the initial rate of change of frequency and steady-state frequency deviation constraints. The study employs improved chaotic mapping and an adaptive weight Particle Swarm Optimization (PSO) algorithm to solve the two-stage optimization model and finally takes the improved IEEE 14-node system as an example to verify the proposed scheme through simulation. Results demonstrate that the proposed method improves the system net load peak-valley difference by 35.9%, controls frequency deviation within ±0.2 Hz range, and reduces generation cost by 7.2%. The proposed optimization scheduling model has high engineering application value. Full article

We present a novel and completely deterministic method to model chaotic orbits in nonlinear discrete dynamics, taking the quadratic map as an example. This method is based on the resurgent analysis developed by Écalle to perform the resummation of divergent power series given by asymptotic expansions in linear differential equations with variable coefficients. To determine the long-term behavior of the dynamics, we calculate the zeros of a function representing the unstable manifold of the system using Newton’s method. The asymptotic expansion of the function is expressed as a kind of negative power series, which enables the computation with high accuracy. By use of the obtained zeros, we visualize the set of homoclinic points. This set corresponds to the Julia set in one-dimensional complex dynamical systems. The presented method is easily extendable to two-dimensional nonlinear dynamical systems such as Hénon maps. Full article

This study conducts an in-depth analysis of the dynamical characteristics and solitary wave solutions of the integrable Zhanbota-IIA equation through the lens of planar dynamic system theory. This research applies Lie symmetry to convert nonlinear partial differential equations into ordinary differential equations, enabling the investigation of bifurcation, phase portraits, and dynamic behaviors within the framework of chaos theory. A variety of analytical instruments, such as chaotic attractors, return maps, recurrence plots, Lyapunov exponents, Poincaré maps, three-dimensional phase portraits, time analysis, and two-dimensional phase portraits, are utilized to scrutinize both perturbed and unperturbed systems. Furthermore, the study examines the power frequency response and the system’s sensitivity to temporal delays. A novel classification framework, predicated on Lyapunov exponents, systematically categorizes the system’s behavior across a spectrum of parameters and initial conditions, thereby elucidating aspects of multistability and sensitivity. The perturbed system exhibits chaotic and quasi-periodic dynamics. The research employs the maximum Lyapunov exponent portrait as a tool for assessing system stability and derives solitary wave solutions accompanied by illustrative visualization diagrams. The methodology presented herein possesses significant implications for applications in optical fibers and various other engineering disciplines. Full article

Early-stage dynamic responses of naval structures under underwater explosion shock loads exhibit high-frequency, intense amplitude fluctuations and short durations, serving as critical factors for the development of plastic deformation and other damage characteristics. These structural dynamics demonstrate prominent nonlinear and non-stationary features. This study focuses on the nonlinear evolutionary patterns of early-stage plastic shock responses in underwater explosion-impacted ship structures. Utilizing phase space reconstruction, unimodal mapping, and symbolic dynamics theory, we analyze the nonlinear and non-stationary characteristics along with their evolutionary patterns in experimental data. First, scaled model experiments under varying shock factors were conducted based on a stiffened cylindrical shell prototype, investigating the spatiotemporal evolution of nonlinear and non-stationary dynamic responses under different shock loads while characterizing their uncertainty features. Second, model tests were performed on deck-type cabin structures and plate frameworks derived from a naval vessel’s deck prototype, further analyzing the evolutionary patterns of early-stage plastic dynamic responses and verifying the method’s effectiveness and universality. Research findings indicate that (1) early-stage plastic shock responses of ships under underwater explosions exhibit multiple dynamical behaviors including chaotic motion, periodic motion, and quasi-periodic motion, and (2) during the initial plastic phase, orbital parameters approximate 0.8, providing guidance for test condition setup and initial parameter selection in underwater explosion experiments on naval structures. Full article

In this study, the complete discrimination system for the polynomial method (CDSPM) is employed to analyze the integrable Gardner Equation (IGE). Through a traveling wave transformation, the model is reduced to a nonlinear ordinary differential equation, enabling the derivation of a wide class of exact solutions, including trigonometric, hyperbolic, rational, and Jacobi elliptic functions. For example, a bright soliton solution is obtained for parameters $A=1.3$, $\beta =-0.1$, and $\gamma =0.8$. Qualitative analysis reveals diverse phase portraits, indicating the presence of saddle points, centers, and cuspidal points depending on parameter values. Chaos and quasi-periodic dynamics are investigated via Poincaré maps and time-series analysis, where chaotic patterns emerge for values like ${\nu }_1=1.45$, ${\nu }_2=2.18$, ${\Xi }_0=4$, and $\lambda =2\pi$. Sensitivity analysis confirms the model’s sensitivity to initial conditions $\chi =2.2,2.4,2.6$, reflecting real-world unpredictability. Additionally, the energy balance method (EBM) is applied to approximate periodic solutions by conserving kinetic and potential energies. These results highlight the IGE’s ability to capture complex nonlinear behaviors relevant to fluid dynamics, plasma waves, and nonlinear optics. Full article

Accurate and efficient short-term load forecasting is crucial for the secure and stable operation and scheduling of power grids. Addressing the inability of traditional Transformer-based prediction models to capture symmetric correlations between different feature sequences and their susceptibility to multi-scale feature influences, this paper proposes a short-term power distribution network load forecasting model based on an enhanced Komodo Mlipir Algorithm (KMA)—Multivariate Variational Mode Decomposition (MVMD)-Crossformer. Initially, the KMA is enhanced with chaotic mapping and temporal variation inertia weighting, which strengthens the symmetric exploration of the solution space. This enhanced KMA is integrated into the parameter optimization of the MVMD algorithm, facilitating the decomposition of distribution network load sequences into multiple Intrinsic Mode Function (IMF) components with symmetric periodic characteristics across different time scales. Subsequently, the Multi-variable Rapid Maximum Information Coefficient (MVRapidMIC) algorithm is employed to extract features with strong symmetric correlations to the load from weather and date characteristics, reducing redundancy while preserving key symmetric associations. Finally, a power distribution network short-term load forecasting model based on the Crossformer is constructed. Through the symmetric Dimension Segmentation (DSW) embedding layer and the Two-Stage Attention (TSA) mechanism layer with bidirectional symmetric correlation capture, the model effectively captures symmetric dependencies between different feature sequences, leading to the final load prediction outcome. Experimental results on the real power distribution network dataset show that: the Root Mean Square Error (RMSE) of the proposed model is as low as 14.7597 MW, the Mean Absolute Error (MAE) is 13.9728 MW, the Mean Absolute Percentage Error (MAPE) reaches 4.89%, and the coefficient of determination (R²) is as high as 0.9942. Full article