Search Results (690)

Macroeconomic mathematical models are practical instruments structured to carry out theoretical analyses of macroeconomic developments. In this manuscript, the Caputo-like fractional operator of variable order is used to introduce and investigate the mechanism of the discrete macroeconomic model. The nature of the dynamics was established, and the emergence of chaos using a distinct variable fractional order, especially the stability of the trivial solution, is examined. The findings reveal that the variable-order discrete macroeconomic model displays chaotic dynamics employing bifurcation, the Largest Lyapunov exponent ($L{E}_{max}$), the phase portraits, and the 0–1 test. Furthermore, a complexity analysis is performed to demonstrate the existence of chaos and quantify its complexity using $C_0$ complexity and spectral entropy ($SE$). These studies show that the suggested variable-order fractional discrete macroeconomic model has more complex features than integer and constant fractional orders. Finally, MATLAB R2024b simulations are run to exemplify the outcomes of this study. Full article

The study of economic maps has consistently attracted researchers due to their rich dynamics and practical relevance. A deeper understanding of these systems enables the development of more effective control strategies. In this work, we examine the influence of the fractional order $\upsilon$ with the Caputo fractional difference on an economic market map. The primary contribution is the comprehensive analysis of how both commensurate and incommensurate fractional orders affect the stability and complexity of the map. Numerical investigations, including phase portraits, largest Lyapunov exponents, and bifurcation analysis, reveal that the system undergoes a cascade of period-doubling bifurcations before transitioning into chaos. To further characterize the dynamics, complexity is evaluated using the 0–1 test and $C_0$ complexity, both confirming chaotic behavior. Furthermore, two-dimensional control schemes are introduced and theoretically validated to both stabilize the chaotic economic market map and achieve synchronization with a combined response map. The theoretical and numerical results are validated through MATLAB 2016 simulations. Full article

We develop and analyze a distributed-delay model for nutrient–fish–mussel dynamics in multitrophic aquaculture systems. Extending the classical discrete-delay framework, we incorporate gamma-distributed kernels to capture the time-distributed nature of nutrient assimilation, yielding a more realistic and analytically tractable representation. These kernels introduce a form of temporal symmetry in the system’s memory, where past nutrient levels influence present dynamics in a balanced and structured way. Using the linear chain trick, we reformulate the integro-differential equations into ordinary differential systems for both weak and strong memory scenarios. We derive conditions for local stability and Hopf bifurcation, and establish global stability using Lyapunov-based methods. Numerical simulations confirm that increased delay can destabilize the system, leading to oscillations, while stronger memory mitigates this effect and enhances resilience. Bifurcation diagrams, time series, and phase portraits illustrate how memory strength governs the system’s dynamic response. This work highlights how symmetry in memory structures contributes to system robustness, offering theoretical insights and practical implications for the design and management of ecologically stable aquaculture systems. Full article

This study applies reinforcement learning to search parameter regimes that yield chaotic dynamics across six systems: the Logistic map, the Hénon map, the Lorenz system, Chua’s circuit, the Lorenz–Haken model, and a custom 5D hyperchaotic design. The largest Lyapunov exponent (LLE) is used as a scalar reward to guide exploration toward regions with high sensitivity to initial conditions. Under matched evaluation budgets, the approach reduces redundant simulations relative to grid scans and accelerates discovery of parameter sets with large positive LLE. Experiments report learning curves, parameter heatmaps, and representative phase portraits that are consistent with Lyapunov-based assessments. Q-learning typically reaches high-reward regions earlier, whereas SARSA shows smoother improvements over iterations. Several evaluated systems possess equation-level symmetry—most notably sign-reversal invariance in the Lorenz system and Chua’s circuit models and a coordinate-wise sign pattern in the Lorenz–Haken equations—which manifests as mirror attractors and paired high-reward regions; one representative is reported for each symmetric pair. Overall, Lyapunov-guided reinforcement learning serves as a practical complement to grid and random search for chaos identification in both discrete maps and continuous flows, and transfers with minimal changes to higher-dimensional settings. The framework provides an efficient method for identifying high-complexity parameters for applications in chaos-based cryptography and for assessing stability boundaries in engineering design. Full article

Background: In the evolving landscape of pathology, Laboratory Information Systems (LISs) have become essential tools for ensuring traceability, efficiency, and data security in diagnostic workflows. Methods: This study presents a comprehensive comparative analysis of three major LIS platforms used in Italian pathology laboratories in 2025: Armonia (Dedalus), Pathox Web (Tesi Group), and WinSAP 3.0 (Engineering). Each system is evaluated across key parameters, including sample traceability, integration with hospital systems, digital reporting, user interface, and compliance with regulatory standards such as GDPR and ISO 15189. Results: Armonia stands out for its advanced integration capabilities, scalability, and support for digital pathology, making it ideal for large institutions. Pathox Web offers a balanced solution with strong usability and web-based accessibility, suitable for medium-sized laboratories. WinSAP 3.0, while more limited in modern features, remains a stable and cost-effective option for many facilities. This study emphasizes the strategic importance of selecting an LIS aligned with institutional needs, highlighting its role in enhancing diagnostic quality, operational safety, and future integration with artificial intelligence and automation. Conclusions: The findings support informed decision-making in LIS adoption, critically contributing to the management of scientific and economic data of pathology services in Italy. Full article

Rheumatoid arthritis (RA) is a heterogeneous autoimmune disease characterized by variable clinical manifestations and a complex, often unpredictable disease trajectory, which hinders early diagnosis and personalized treatment. This review highlights recent breakthroughs in biomarker discovery, emphasizing the transformative impact of multi-omics technologies and deep profiling of the synovial microenvironment. Advances in genomics and transcriptomics have identified key genetic variants and expression signatures associated with disease susceptibility, progression, and therapeutic response. Complementary insights from proteomics and metabolomics have elucidated dynamic molecular patterns linked to inflammation and joint destruction. Concurrently, microbiome research has positioned gut microbiota as a compelling source of non-invasive biomarkers with both diagnostic and immunomodulatory relevance. The integration of these diverse data modalities through advanced bioinformatics platforms enables the construction of comprehensive biomarker panels, offering a multidimensional molecular portrait of RA. When coupled with synovial tissue profiling, these approaches facilitate the identification of spatially resolved biomarkers essential for localized disease assessment and precision therapeutics. These innovations are transforming RA care by enabling earlier detection, improved disease monitoring, and personalized treatment strategies that aim to optimize patient outcomes. Full article

This paper introduces an analytical framework, complex mathematical personhood, to broaden understandings of how teacher identity is developed over time through an emancipatory lens. A single case study, or portrait, is shared of a Native Hawaiian middle school mathematics teacher who uses Indigenous and ethno-mathematical practices to inform his instruction. A bricolage of case study and portraiture methods was invoked as the methodological framework for this project. Key results demonstrate the importance of broadening mathematics teaching practices that center and reorient de/colonial practices in teacher pedagogical orientations. Full article

Higher education is often positioned as a pathway to upward social mobility, yet access to highly selective universities (HSUs) remains limited, with first-generation college (FGC) students from low-income and ethnoracially minoritized backgrounds disproportionately constrained by structural barriers. This study applies an asset-based lens to examine how a cross-generational team of six Latine FGC affiliates of an HSU (i.e., alumni, doctoral students, professor) resiliently persisted in their educational and professional journeys, leveraging cultural and social capital. Employing Chicana/Latina feminist methodology and dialogic inquiry, we engaged in pláticas to critically reflect on factors that shaped our life trajectories. Findings reveal that social mobility was negotiated collectively rather than individually, highlighting tensions between personal advancement and commitments to family and community. We also consider the role of structured happenstance in pivotal encounters (e.g., being recognized by mentors, recruited by scholarship programs) that appeared serendipitous but were situated within systems where opportunity is inequitably distributed. Structured happenstance exposes the precariousness of such pathways and systemic gaps in FGC student support, challenging the notion that access to elite, capital-rich institutions is the product of merit alone. Our narratives offer a nuanced portrait of how FGC students navigate social mobility across the life course. Full article

This study investigates how the addition of a carbon-based filler obtained through the pyrolysis of medium-density fibreboard (MDF) waste affects the mechanical behaviour of epoxy–glass laminates. Two laminate series with different matrix-to-reinforcement ratios (60/40 and 65/35) were fabricated and modified with carbonised particles of up to 500 μm in size, introduced at 5% and 7.5%. The strength of the samples made of the materials mentioned above was assessed in a static three-point bending test by analysing the values of stresses (${\sigma }_{fM}$) and strains (${\epsilon }_{fM}$). For an in-depth analysis of the dynamics of the destruction process, the recorded deformation data were subjected to Kolmogorov–Sinai metric entropy ($E_{K-S}$). The test results showed that the addition of carbonisate in series A (60/40) increased the flexural strength by 32.56% for the sample with 5% addition and by 27.08% for the sample with 7.5% addition, compared to the reference material. In series B (65/35), characterised by a higher resin content, the opposite effect was observed—a decrease in strength of 9.89% (for 5% carbonisate) and 15.53% (for 7.5% carbonisate). The use of $E_{K-S}$ calculations in combination with phase portrait reconstruction to analyse the results obtained allowed for the precise determination of the limit values of stresses and strains (${\sigma }_{fMK\_S}$ and ${\epsilon }_{fMK\_S}$) at which irreversible structural changes occur in the material, initiating the destruction process. This method proved to be an effective tool for identifying early signs of composite degradation, which is crucial for assessing its long-term strength and designing safe structures. Full article

This study presents a mathematical model to understand the dynamics of eye vision disability, incorporating key physiological and environmental variables such as visual acuity, lens power, pupil diameter, and environmental influence. The novel model developed in this work consists of four state variables that describe their interactions, aiming to simulate changes in visual acuity and the progression of vision disability under different circumstances. Various mathematical aspects including positivity and equilibrium points along with local and global stability are demonstrated. In addition, the sensitivity analysis is also presented to examine the impact of variations in parameters on the model’s outcomes, highlighting the factors that significantly influence visual acuity and pupil adjustments. Furthermore, the phase portraits explore the dynamic interactions between variables, revealing different insights into the stability of the system and adaptive responses. These results provide a thorough understanding of factors influencing eye vision, offering new insights into vision disability dynamics through an integrated, non-autonomous model and practical applications in developing corrective strategies. Full article

Clear-air turbulence (CAT), as a key meteorological hazard threatening aviation safety, urgently requires the revelation of its spatiotemporal distribution patterns and formation mechanisms within the China region. Based on the first release of 12,539 aircraft turbulence voice reports from China’s civil aviation from 2022 to 2024 and ERA5 high-resolution reanalysis data, this study constructs for the first time a climatological portrait of aircraft turbulence over China, revealing the spatiotemporal distribution characteristics and formation mechanisms of CAT in the region: turbulence occurs predominantly at 3000–8000 m (accounting for 61.0%), peaking at 7000–8000 m, driven by strong low-level jet wind shear and Kelvin–Helmholtz instability (KHI); wintertime exhibits a high frequency (33.4%) stemming from strong upper-level jets (>30 m s⁻¹), while summer is dominated by low-level thermal convection (21.0%); the high-incidence zones of Central-South and Southwest China (>2800 events) are jointly governed by a mid-level strong horizontal gradient of vertical vorticity, divergence perturbations, and jet shear, with the winter jet shifting southward (22–30° N), further intensifying the turbulence risk. The findings establish a dynamic–thermodynamic coupling mechanism for CAT over China, providing a scientific basis for aviation safety early warning. Full article

Wearable devices (WDs) are increasingly integrated into clinical workflows to enable continuous, non-invasive vital signs monitoring. Combined with Artificial Intelligence (AI), these systems can shift clinical monitoring from being reactive to predictive, allowing for earlier detection of deterioration and more personalized interventions. The value of these technologies lies not in absolute measurements, but in detecting physiological parameters trends relative to each patient’s baseline. Such a trend-based approach enables real-time prediction of deterioration, enhancing patient safety and continuity of care. However, despite their shared multiparametric capabilities, WDs are not interchangeable. This narrative review analyzes nine clinically validated devices, Radius VSM^® (Masimo Corporation, Irvine, CA, USA), BioButton^® (BioIntelliSense Inc., Redwood City, CA, USA. Distributed by Medtronic), Portrait Mobile^® (GE HealthCare, Chicago, IL, USA), VitalPatch^® (VitalConnect Inc., San Jose, CA, USA), CardioWatch 287-2^® (Corsano Health B.V., The Hague, The Netherlands. Distributed by Medtronic), Cosinuss C-Med Alpha^® (Cosinuss Gmb, Munich, Germany), SensiumVitals^® (Sensium Healthcare Limited, Abingdon, Oxfordshire, UK), Isansys Lifetouch^® (Isansys Lifecare Ltd., Abingdon, Oxfordshire, UK), and CheckPoint Cardio^® (CheckPoint R&D LTD., Kazanlak, Bulgaria), highlighting how differences in sensor configurations, battery life, connectivity, and validation contexts influence their suitability across various clinical environments. Rather than establishing a hierarchy of technical superiority, this review emphasizes the importance of context-driven selection, considering care setting, patient profile, infrastructure requirements, and interoperability. Each device demonstrates strengths and limitations depending on patient population and operational demands, ranging from perioperative, post-operative, emergency, or post-Intensive Care Unit (ICU) settings. The findings support a tailored approach to WD implementation, where matching device capabilities to clinical needs is key to maximizing utility, safety, and efficiency. Full article

Computer viruses remain a persistent technological challenge in information security. They require mathematical frameworks that realistically capture their propagation in digital networks. Classical continuous-time, integer-order models often overlook two key aspects of cyber environments: their inherently discrete nature and the memory-dependent effects of networked interactions. In this work, we introduce a fractional-order discrete computer virus (FDCV) model, derived from a three-dimensional continuous integer-order formulation and reformulated into a two-dimensional fractional discrete framework. We analyze its rich dynamical behaviors under both commensurate and incommensurate fractional orders. Leveraging a comprehensive toolbox including bifurcation diagrams, Lyapunov spectra, phase portraits, the 0–1 test for chaos, spectral entropy, and $C_0$ complexity measures, we demonstrate that the FDCV system exhibits persistent chaos and high dynamical complexity across broad parameter regimes. Our findings reveal that fractional-order discrete models not only enhance the dynamical richness compared to integer-order counterparts but also provide a more realistic representation of malware propagation. These insights advance the theoretical study of fractional discrete systems, supporting the development of potential technologies for cybersecurity modeling, detection, and prevention strategies. Full article

In this paper, we investigate the generalized coupled Zakharov system (GCZS), a fundamental model in plasma physics that describes the nonlinear interaction between high-frequency Langmuir waves and low-frequency ion-acoustic waves, including the influence of magnetic fields on weak ion-acoustic wave propagation. This research aims to achieve three main objectives. First, we uncover soliton solutions of the coupled system in hyperbolic, trigonometric, and rational forms, both in single and combined expressions. These results are obtained using the extended rational sinh-Gordon expansion method and the $\left({\displaystyle \frac{G^{\prime }}{G}},{\displaystyle \frac{1}{G}}\right)$-expansion method. Second, we analyze the dynamic characteristics of the model by performing bifurcation and sensitivity analyses and identifying the corresponding Hamiltonian function. To understand the mechanisms of intricate physical phenomena and dynamical processes, we plot 2D, 3D, and contour diagrams for appropriate parameter values. We also analyze the bifurcation of phase portraits of the ordinary differential equations corresponding to the investigated partial differential equation. The novelty of this study lies in the fact that the proposed model has not been previously explored using these advanced methods and comprehensive dynamical analyses. Full article

Fractional-order chaotic systems have received increasing attention over the past few years due to their ability to effectively model memory and complexity in nonlinear dynamics. Nonetheless, most of the research conducted so far has been on constant-order formulations, which still have some limitations in terms of adaptability and reality. Thus, to evade these limitations, we present a recently designed four-dimensional hyperchaotic Chen system with variable-order fractional (VOF) derivatives in the Liouville–Caputo sense. In comparison with constant-order systems, the new system possesses excellent performance in numerous aspects. Firstly, with the use of variable-order derivatives, the system becomes more adaptive and flexible, allowing the chaotic dynamics of the system to evolve with changing fractional orders. Secondly, large-scale numerical simulations are conducted, where phase portrait orbits and time series for differences in VOF directly illustrate the effect of the order function on the system’s behavior. Thirdly, qualitative analysis is performed with the help of phase portraits, time series, and Lyapunov exponents to confirm the system’s hyperchaotic behavior and sensitivity to initial and control parameters. Finally, the model developed demonstrates a wide range of dynamic behaviors, which confirms the sufficient efficiency of VOF calculus for modeling complicated nonlinear processes. Numerous analyses indicate that this research not only shows meaningful findings but also provides thoughtful methodologies that might result in subsequent research on fractional-order chaotic systems. Full article