Search Results (2,228)

This paper investigates a discrete diffusion carbon emission-absorption model with periodic boundary conditions derived via the piecewise constant argument scheme. The existence of equilibrium points is established, and sufficient conditions for the local asymptotic stability of the positive equilibrium are derived through eigenvalue analysis. Then, uniform boundedness of positive solutions is proved, and the global asymptotic stability of the interior equilibrium is established by an iterative method and the comparison principle for difference equations. Furthermore, the model is shown to undergo a flip bifurcation when a critical parameter threshold is reached, leading to period-doubling dynamics and chaotic behavior. The influence of spatial diffusion is examined through a Turing instability analysis, yielding conditions for diffusion-driven instability and spatial pattern formation. Finally, Decision Tree and Random Forest classifiers are used as proof-of-concept tools to efficiently approximate the analytically derived stability regions using Monte Carlo-generated data. Both classifiers successfully reproduce the analytical stability structure, while the Random Forest classifier provides higher accuracy and smoother stability boundaries. Numerical simulations support the theoretical results and illustrate the stability and bifurcation phenomena exhibited by the model. These findings indicate that the proposed framework is useful for analyzing carbon emission-absorption dynamics and that machine learning can serve as an efficient computational surrogate for identifying stability regions in nonlinear dynamical systems. Full article

Meta-analysis is a statistical tool commonly used within systematic reviews to synthesize quantitative evidence, but individual studies with atypical results or disproportionate influence can materially affect pooled estimates, heterogeneity estimates, and the conclusions drawn from evidence syntheses. Conventional outlier and influence diagnostics for meta-analysis are useful, but their interpretation often relies on asymptotic reference values or informal rules of thumb, which may be inadequate when the number of studies is limited or heterogeneity is substantial. We introduce boutliers, an R package that implements bootstrap-calibrated outlier detection and influence diagnostics for fixed-effect and random-effects meta-analysis. The package provides leave-one-study-out diagnostics based on Studentized deleted residuals, relative changes in the variance of the pooled effect estimator, and relative changes in the between-study variance, together with a likelihood-ratio diagnostic based on a mean-shifted model. For each diagnostic measure, bootstrap reference distributions, critical values, and p-values are provided to support quantitative interpretation of influential studies. We describe the statistical framework, implementation, and practical use of the package and illustrate its application using a real published meta-analysis dataset on spinal manipulative therapy for chronic low back pain. The boutliers package provides accessible tools for incorporating uncertainty-calibrated influence diagnostics into routine meta-analytic practice. Full article

This study develops an analytical and computational framework for coupled transient gas redistribution induced by simultaneous localized injection and withdrawal in transmission pipelines. The aim is to describe source–sink interactions within a single transmission system, unlike conventional approaches that treat inflow and outflow processes independently. The governing equations of one-dimensional non-stationary isothermal compressible gas flow are transformed into a diffusion-type formulation using Charny regularization. The pipeline is divided into three interacting regions connected through pressure-continuity and mass-flux coupling conditions. Closed-form Laplace-domain solutions are derived for the dimensionless pressure field, and a practical Laplace-domain approximation is used for computational evaluation of transient pressure profiles. The results reveal a characteristic balancing point separating injection-dominated and withdrawal-dominated regions and show rapid convergence toward a quasi-steady redistribution regime. A pressure-deviation-based objective function is introduced to evaluate hydraulic disturbance, and the optimization analysis shows that the minimum disturbance occurs under a near-balanced source–sink operating condition. The obtained pressure profiles, asymptotic behavior, and regional redistribution patterns confirm the physical consistency of the proposed model. The framework provides a mathematically interpretable basis for analyzing coupled redistribution dynamics, hydraulic stabilization, and asymptotic equilibrium in gas transmission systems. Full article

Regular black-hole models replace the Schwarzschild singularity with a finite inner core, thereby removing the geometric endpoint at which the classical spacetime description breaks down. This issue is relevant to black-hole quantum information, since a singular interior prevents a regular effective description of interior degrees of freedom and horizon correlations. In this work, the regular black-hole geometry introduced by Dymnikova is used as a compact, single-scale effective background for black-hole quantum information considerations. The aim is not to propose a new regular metric but to clarify how an established finite-core geometry can support a nonsingular description of the Schwarzschild interior at the effective level. The geometry preserves the Schwarzschild asymptotic limit while replacing the divergent central region with a finite de Sitter-like core. The curvature invariants remain finite, and the effective source admits an anisotropic-fluid interpretation whose central limit is isotropic and vacuum-like. This use therefore provides a minimal geometric setting, rather than a newly proposed metric solution, for discussing nonsingular black-hole interiors. It does not establish unitary evaporation, information recovery, dynamical stability, or a microscopic quantum-gravity mechanism. Instead, it identifies a finite-curvature spacetime framework in which questions concerning interior quantum degrees of freedom and horizon entanglement can be formulated without encountering a curvature singularity. Full article

In this work, we use the Riemann–Liouville (R-L) fractional derivative of order $\alpha \in (0,1)$ to study the oscillation criteria for damped matrix fractional differential equations and determine sufficient conditions under which all prepared solutions of the system show oscillatory behaviour. The criteria are novel even for the linear undamped case and extend conventional oscillation results for integer-order matrix differential systems to the fractional setting. The goal of the current effort is to better understand the relationships between solutions and their derivatives. Using the matrix-valued Riccati transformation converts the system into a Riccati-type inequality, and the oscillation conditions are then derived by integrating against a weighted kernel via the operator L. Both results generalise the integer-order oscillation criteria to the fractional matrix setting, extending their applicability to fractional-order control systems, viscoelastic structural models, and anomalous diffusion processes. This work develops new conditions and analytical techniques that deepen insight and provide useful results for analysing oscillatory behaviour and asymptotic stability of of the considered systems. To illustrate the significance of the obtained oscillation results, we give two examples. Full article

The parameter space in a regression model for multinomial time series data contains the regression parameters those explain the effects of the time dependent covariates, and the dynamic dependence or category transition parameters those explain the influence of the past responses on the multinomial response at a given time. The estimation of the regression parameters can be negatively affected when higher dimension of the parameter space is considered specially for the transition parameters. In this paper we propose a parameter dimension-split approach where a conditional generalized quasi-likelihood (CGQL) estimating function is first developed for the dynamic dependence parameters in terms of unknown regression parameters which is exploited in the next step to develop an observed information matrix based maximum likelihood (ML) estimating equation for the main regression parameters. More specifically, this split approach helps to write the actual joint likelihood function of regression and dynamic dependence parameters as a likelihood function of regression parameters only by replacing the dynamic dependence parameters with their CGQL estimates obtained in the first step. As the time series length is generally large in practice, we have made sure that the proposed CGQL and ML estimators are asymptotically reliable, that is consistent for the respective parameters. Full article

A nonlinear backstepping control framework is developed for autonomous landing of a quadrotor on a wave-excited marine platform. This study addresses the underactuated nature of the aerial vehicle and the strong coupling between translational and rotational dynamics, ensuring stable trajectory tracking under sea-induced disturbances. Reference trajectories are generated through physically grounded Pierson–Moskowitz (PM) and modified Pierson–Moskowitz (MPM) wave spectra, enabling realistic modeling of vertical heave motion, while horizontal position and yaw are defined through harmonic components adapted to the sea-state regime. The controller is designed through a seven-step recursive backstepping procedure, with Lyapunov functions guaranteeing asymptotic stability of the tracking errors for the regulated outputs. A modular MATLAB simulation platform is implemented, integrating the full six-DOF quadrotor dynamics, the control algorithm, and spectral reference generation. Numerical simulations demonstrate that the Lyapunov function derivatives remain negative over the entire simulation horizon, confirming asymptotic convergence. Comparative results with a tuned PID (proportional integral derivative) controller indicate superior tracking performance and damping and reduced amplitude and phase errors for the backstepping approach, especially under MPM-based trajectories representing rough sea states. The proposed framework establishes a reliable basis for adaptive extensions and future hardware-in-the-loop validation of autonomous landing on moving marine platforms. Full article

In this manuscript, the stability characteristics of nonlinear nonautonomous dynamical systems with the newly defined Caputo cotangent fractional derivative (CCFD) are discussed. Conditions that guarantee stability and asymptotic stability of the system are developed through comparison methods for CCFD systems using Lyapunov functions. A quadratic inequality for the CCFD and a sign lemma are established as key analytical tools. The additional parameter $r_2$ continuously recovers the classical Caputo derivative at $r_2=1$ and introduces an exponential attenuation mechanism when $0<r_2<1$. Analytical examples and a reproducible numerical trajectory study illustrate the influence of $r_2$ on the decay of solutions. The results extend classical Lyapunov stability theory to a broader class of nonlinear fractional systems and suggest modeling opportunities in systems where power-law memory and exponential attenuation coexist. Full article

This paper formulates a latent HIV infection model with saturated immunity, two general infection rates (virus-to-cell and cell-to-cell transmission), and three time delays (infected cell activation delay, virus production delay, and immune response delay). The dynamical behaviors and equilibria stability of the model are theoretically analyzed. By constructing appropriate Lyapunov functions, sufficient conditions for the global asymptotic stability of the infection-free, immune-free, and coexistence equilibria are derived. All theoretical results are validated using numerical simulations. The simulation results reveal the difficulty of suppressing HIV infection for cases with a sufficiently large basic reproduction number. For patients with a high basic reproduction number, a single therapeutic strategy that only enhances the reversion rate of latently infected cells may not be effective. Full article

East Coast Fever (ECF) causes approximately one million livestock deaths annually in sub-Saharan Africa, posing a significant threat to livestock. The wildlife–livestock interface complicates disease management, as wildlife serve as reservoirs. This study developed a Continuous Time Markov Chain (CTMC) model incorporating the wildlife–livestock interface to analyze ECF dynamics. Using the Galton–Watson approximation, we assessed the probability of disease extinction following the introduction of infected hosts or vectors. The probability of disease extinction calculated from the branching process is shown to be in good agreement with the probability approximated from numerical simulations. The disease dynamics of the deterministic model and the CTMC model are compared to ascertain the effect of demographic stochasticity on ECF dynamics. Differences in model predictions and asymptotic dynamics between stochastic and deterministic models were evident. The deterministic and stochastic formulations should therefore be viewed as complementary modeling frameworks, with the deterministic model characterizing average epidemic dynamics and the CTMC model capturing the probabilistic variability and extinction behavior inherent in real transmission processes. These differences are crucial for intervention strategies earmarked to prevent outbreaks. Our analysis revealed a high probability of ECF extinction if the disease emerges from recovered carrier cattle. Finite time to ECF disease extinction is estimated using 10,000 sample paths, and it is shown that the epidemic duration is shortest if the disease is introduced by infectious cattle. The epidemic duration is longest when the disease is introduced by infectious ticks. Additionally, we observed that host interactions at the wildlife–livestock interface play a critical role in shaping ECF transmission and informing control strategies. Full article

Advancement toward the Essential Science Indicators (ESI) Top 1‰ is an important indicator of disciplinary competitiveness, but progress near this boundary is often nonlinear because the global threshold continues to move upward. This study develops a two-layer framework combining an Exponential Decay Model (EDM) for modeling rank trajectories and a Bivariate Logarithmic Difference Decomposition Model (BLDDM) for separating institutional citation growth from external threshold pressure. Using 13 bimonthly ESI update waves from March 2024 to March 2026, we analyze Chemistry, Engineering, and Materials Science at Wuhan Institute of Technology. The results show that the EDM outperforms a linear benchmark in all three disciplines, indicating an asymptotic pattern of advancement near the Top 1‰ boundary. The BLDDM further reveals substantial disciplinary heterogeneity: Engineering faces the strongest threshold pressure, whereas Chemistry is the most favorable near-term candidate for breakthrough. These findings suggest that ESI advancement should be understood as a moving-threshold process rather than a simple accumulation of citations. Full article

This paper presents a mechanistic model for a thin-layer microalgal bioreactor cultivating Stigeoclonium nanum, with a comprehensive analysis of its dynamics and stability. Unlike most bioreactor studies that assume simple Monod or linear growth, our model rigorously explores the nonlinear interplay between logistic constraints and multiple nutrient limitations. We introduce a coupled Logistic–Monod system of nonlinear ordinary differential equations that captures sigmoidal transitions and steady states of Stigeoclonium nanum under simultaneous nitrogen and phosphorus depletion and incorporates abiotic nutrient removal to ensure mass conservation. Qualitative analysis proves positive invariance and boundedness of solutions using the Localization of Compact Invariant Sets method. Asymptotic stability of the biologically relevant equilibrium is established. Experimental validation in a thin-layer photobioreactor using three-fold cross-validation yielded high correlation coefficients (0.78–0.96) for biomass, nitrate, and phosphate concentrations, confirming predictive accuracy. The model thus provides a robust framework for process control and optimization in industrial-scale applications. Full article

This work investigates the complex dynamics of two novel Holling type II predator–prey (PP) models under the impact of climate change and controlled by the Caputo and Caputo–Fabrizio fractional operators. Here, Holling type II and static changes are considered using the first PP model, while the other PP model is considered when periodic changes over time are employed. In the presence of each fractional operator, the stability analysis of all equilibrium states is studied, and the conditions of asymptotically stability are obtained. The numerical results showed considerable variability in the complex dynamics of these models using both operators. Furthermore, a comparison of the numerical results showed that the Caputo–Fabrizio operator is better than the Caputo operator in describing the complex dynamics of the second model because the scenarios displaying chaos regions when using the Caputo–Fabrizio operator occur over wider ranges than their counterparts when using the Caputo operator. With the memory effect present, the results show an improvement in system stability and thus an increased survival possibility despite the presence of adverse climatic conditions in the environment. Full article

Poisson mixed-effects models are essential for analyzing repeated count data, relying on latent random effects to account for unobserved heterogeneity and longitudinal dependence. However, the validity of likelihood-based inference in these models is highly sensitive to the specification of both the fixed-effects structure and the distributional assumptions of the random effects. While diagnostics based on the information matrix equality (IME) provide a theoretical framework for detecting misspecification, their high dimensionality and reliance on second-order derivatives often result in numerical instability and poor finite-sample performance in nonlinear settings. Here we introduce the Contrast of Information by Volume (CIV) test, a low-dimensional information-based diagnostic test for Poisson generalized linear mixed models (GLMMs). By integrating the scalar CIV statistics with novel graphical diagnostics, our approach facilitates the interpretation of specification errors in the random-effects structure. We derive the asymptotic behaviour of the CIV statistics under local misspecification and evaluate their properties through Monte Carlo simulations. To ensure robust inference in moderate samples, a parametric bootstrap procedure is employed for size calibration. Simulation results demonstrate that the CIV diagnostics maintain accurate Type I error control and achieve competitive power against common misspecification, including heteroskedasticity, correlation, and heavy-tailed random-effect distributions. Compared to traditional IME diagnostics, estimator-comparison tests, and GMM-based procedures, the CIV approach offers a superior balance between finite-sample stability and detection power. Finally, an empirical application illustrates the utility of the CIV framework in diagnosing latent misspecification and guiding the selection of random-effects covariance structures in applied research. Full article

Brucellosis remains a significant public health and economic burden in many regions, primarily transmitted from livestock to humans through direct contact and environmental contamination. In this paper, we develop a novel cross-species epidemic model that couples the transmission dynamics of brucellosis among sheep, humans, and the environmental reservoir of Brucella. The sheep population is divided into susceptible, exposed, infectious, and vaccinated compartments, while the human population is stratified into susceptible and infected classes. Environmental brucella load is explicitly modeled, and distributed time delays are incorporated to account for incubation periods and delayed exposure risks in humans. We prove that all solutions are non-negative and ultimately bounded, ensuring biological consistency. The basic reproduction number ${\mathcal{R}}_0$ is derived using the next-generation matrix method. Using Lyapunov functionals and LaSalle’s invariance principle, we establish that the disease-free equilibrium is globally asymptotically stable when ${\mathcal{R}}_0\le 1$, whereas a unique endemic equilibrium exists and is globally asymptotically stable when ${\mathcal{R}}_0>1$. Sensitivity analysis identifies the environmental transmission rate, shedding rate, and disinfection as the most influential parameters. Treatment efficacy is shown to exhibit a critical threshold $p^{\mathrm{cr}}=1-1/{\mathcal{R}}_0$, above which eradication becomes feasible. Numerical simulations validate the theoretical findings and demonstrate that time delays affect outbreak timing but not asymptotic stability. These results provide quantitative guidance for brucellosis control strategies, emphasizing environmental sanitation, culling, and vaccination as key interventions. Full article