Search Results (256)

We present a comprehensive mathematical analysis of a within-host dual-target HIV dynamics model, which explicitly incorporates the virus’s interactions with its two primary cellular targets: CD4${}^{+}$ T cells and macrophages. The model is formulated as a system of five nonlinear delay differential equations, integrating three distinct discrete time delays to account for critical intracellular processes such as the development of productively infected cells and the maturation of new virions. We first establish the model’s biological well-posedness by proving the non-negativity and boundedness of solutions, ensuring all trajectories remain within a feasible region. The basic reproduction number, ${\mathcal{R}}_0^d$, is derived using the next-generation matrix method and serves as a sharp threshold for disease dynamics. Analytical results demonstrate that the infection-free equilibrium is globally asymptotically stable (GAS) when ${\mathcal{R}}_0^d\le 1$, guaranteeing viral eradication from any initial state. Conversely, when ${\mathcal{R}}_0^d>1$, a unique endemic equilibrium emerges and is proven to be GAS, representing a state of chronic infection. These global stability properties are rigorously established for both the non-delayed and delayed systems using carefully constructed Lyapunov functions and functionals, coupled with LaSalle’s invariance principle. A sensitivity analysis identifies viral production rates ($p_1,p_2$) and infection rates (${\beta }_1,{\beta }_2$) as the most influential parameters on ${\mathcal{R}}_0^d$, while the viral clearance rate (m) and maturation delay (${\tau }_3$) have a suppressive effect. The model is extended to evaluate antiretroviral therapy (ART), revealing a critical treatment efficacy threshold ${ϵ}^{cr}$ required to suppress the virus. Numerical simulations validate all theoretical findings and further investigate the dynamics under varying treatment efficacies and maturation delays, highlighting how these factors can shift the system from persistence to clearance. This study provides a rigorous mathematical framework for understanding HIV dynamics, with actionable insights for designing targeted treatment protocols aimed at achieving viral suppression. Full article

In this paper, we consider Cover’s and Pombra’s formulation of feedback capacity of additive Gaussian noise (AGN) channels, with jointly Gaussian nonstationary and nonergodic noise. We derive closed-form feedback capacity formulas, using Karush–Kuhn–Tucker (KKT) conditions and convergence properties of difference Riccati equations to limiting algebraic Riccati equations of filtering theory, for unstable and stable autoregressive (AR) noise. Surprisingly, the capacity formulas depend on the parameters of the AR noise, its pole $c\in (-\infty ,\infty )$ and noise variance $K_W\in (0,\infty )$, and the total transmit power $\kappa \in [0,\infty )$, indicating substantial gains for the unstable noise region $\forall c^2\in (1,\infty ),\forall \kappa >{\kappa }_{min}\stackrel{▵}{=}{\displaystyle \frac{K_W\left(1+\sqrt{4c^2-3}\right)}{2{\left(c^2-1\right)}^2}}$ compared to its complement region. In particular, feedback capacity is distinguished by three regimes, as follows. Regime 1, $\forall c^2\in (1,\infty ),\forall \kappa >{\kappa }_{min}$: the optimal channel input includes an innovations part, the capacity increases as $\left|c\right|>1$ increases, while ${\kappa }_{min}$ and the allocated transmit power decrease. Regime 2, $\forall c^2\in (1,\infty ),\forall \kappa \le {\kappa }_{min}$, Regime 3, $\forall c\in [-1,1],\forall \kappa \in [0,\infty )$ (complement of Regime 1): the innovations part of the optimal channel is asymptotically zero and the capacity is fundamentally different compared to Regime 1. The differences of capacity formulas for Regimes 1, 2 and 3 are directly related to their operational meaning: (i) Regime 1 is an ergodic capacity while Regimes 2 and 3 are nonergodic capacities; (ii) Regime 1 is achieved by an asymptotically stationary channel input with a non-zero innovations part, while Regimes 2 and 3 are achieved by an asymptotically zero innovations part. The gains of capacity for Regime 1 are attributed to the high correlation of noise samples compared to stable noise and the use of an informative innovations part by the optimal channel input, which make possible the prediction of future noise samples from past samples, unlike memoryless noise. Our results provide answers to certain open questions regarding the validity of capacity formulas of stable noise that appeared in the literature. Full article

This paper focuses on designing an event-triggered dynamic output feedback controller for discrete-time linear systems subject to actuator and sensor constraints as well as external disturbances. A dynamic event-triggered condition with two generalized weighting parameters is introduced to regulate sensor-to-controller communication. By integrating generalized sector conditions, Lyapunov analysis, and linearization techniques, sufficient conditions are derived in terms of linear matrix inequalities, ensuring bounded closed-loop trajectories, prescribed $H_{\infty }$ performance, and asymptotic stability in the disturbance-free case. Furthermore, optimization problems are formulated to maximize the event-triggering rate while preserving the desired system performance. Simulation results show that, compared to time-triggered control, the event-triggered control effectively reduces the communication frequency, thereby significantly conserving communication resources. Compared with existing results, this work presents the first event-triggered dynamic output feedback scheme for discrete-time linear systems with dual saturation constraints. The inclusion of generalized weighting parameters and the use of generalized sector conditions allow the design to be carried out within a flexible local framework with reduced conservatism. Full article

In this paper, we study the local stability of an incommensurate fractional reaction–diffusion glycolysis model. The glycolysis process, fundamental to cellular metabolism, exhibits complex dynamical behaviors when formulated as a nonlinear reaction–diffusion system. To capture the heterogeneous memory effects often present in biochemical and chemical processes, we extend the classical model by introducing incommensurate fractional derivatives, where each species evolves with a distinct fractional order. We linearize the system around the positive steady state and derive sufficient conditions for local asymptotic stability by analyzing the eigenvalues of the associated Jacobian matrix under fractional-order dynamics. The results demonstrate how diffusion and non-uniform fractional orders jointly shape the stability domain of the system, highlighting scenarios where diffusion destabilizes homogeneous equilibria and others where incommensurate memory effects enhance stability. Numerical simulations are presented to illustrate and validate the theoretical findings. Full article

The very flexible Weibull (VF-W) distribution is formulated by expressing its cumulative risk function as a logarithmic composite of auxiliary cumulative risks, making the model particularly well-suited for modeling heterogeneous life behaviors. This model admits a remarkably flexible hazard structure, capable of generating monotone increasing, unimodal (increase-then-decrease), and multi-turning-point shapes, thereby capturing complex failure behaviors far beyond those allowed by the classical Weibull distribution. This paper presents a comprehensive inferential study of the VF-W model through the unified progressive hybrid (UPH) censoring framework for modeling shock-type lifetime data. The UPH scheme integrates the advantages of Type-II, generalized hybrid, and progressive hybrid censoring mechanisms into a unified structure that ensures efficiency and adaptability in reliability testing. Classical inference is developed through maximum likelihood estimation with asymptotic interval construction, while Bayesian inference is performed using independent gamma priors and a Markov iterative algorithm. Extensive Monte Carlo experiments are conducted to evaluate the finite-sample performance of both approaches under various censoring intensities, revealing that the Bayesian MCMC-based estimators and their highest posterior density intervals provide superior precision, coverage, and robustness. The proposed VF-W model using UPH-based strategy is further validated through the analysis of a real shocks dataset, where it demonstrates a comparative performance improvement over existing models. The VF-W model exhibits stable parameter estimation under diverse censoring levels, indicating robustness in incomplete-data scenarios. Furthermore, the model maintains analytical tractability, offering closed-form expressions for key reliability measures, which facilitates practical implementation in different scenarios. The results confirm the VFW model’s strong potential as a unifying and computationally stable tool for reliability modeling, particularly in complex engineering and physical systems operating under stochastic shock environments. Full article

Controllability metrics based on system Gramians have been widely adopted to provide quantitative measures of the degree of controllability (DoC) and the disturbance rejection capability (DoDR) of dynamical systems. While steady-state Gramian formulations offer closed-form tractability, they are not applicable when rigid-body modes are present, as the associated poles at the origin cause the conventional Gramians to diverge. This paper presents a novel steady-state DoDR metric for linear time-invariant systems with a rigid-body mode. By block-diagonalizing the dynamics through a similarity transformation and analyzing the asymptotic behavior of the Gramian matrices, we derive an exact closed-form expression for the steady-state DoDR. The resulting formulation is numerically stable and enables systematic evaluation of disturbance-rejection capability even in the presence of a rigid-body mode. The proposed metric is validated using a mass–spring–damper chain model, where its effectiveness is demonstrated in actuator placement problems. The results show that the metric not only remains computationally well-posed but also provides physically meaningful interpretations consistent with modal characteristics. This study establishes a foundation for extending disturbance-rejection metrics to systems with multiple rigid-body modes, thereby broadening the applicability of Gramian-based controllability analysis. Full article

This paper presents an approach to the velocity control loop of induction motor drives utilizing the Higher-Order PID-Nested Nonsingular Terminal Sliding Mode (PID-NTSM) method. Here, the PID-NTSM sliding manifold is formulated by the incorporation of both derivative and integral errors of states into the conventional nonsingular terminal sliding mode surface (NTSM). In this manner, the control signals take the higher-order sliding mode control law, obtained by multiple integrals. In this way, such signals are continuous, and the sliding manifold is obtained in finite time; the system’s states asymptotically converge chattering-free to zero at a much faster response time and higher tracking precision while maintaining inherited robustness characteristics. The effectiveness of the proposed method is comprehensively validated both numerically and experimentally. Full article

Tomato Yellow Leaf Curl Virus (TYLCV) has recently caused severe economic losses in global tomato production. According to the International Plant Protection Convention (IPPC), yield reductions of 50–60% have been reported in several regions, including the Caribbean, Central America, and South Asia, with losses in sensitive cultivars reaching up to 90–100%. In developing countries, TYLCV and mixed infections affect more than seven million hectares of tomato-growing land annually. In this study, we construct and analyze a nonlinear dynamic model describing the transmission of TYLCV, incorporating the Caputo fractional-order derivative operator. The existence and uniqueness of solutions to the proposed model are rigorously established. Equilibrium points are identified, and the Jacobian determinant approach is applied to compute the basic reproduction number, $R_0$. Suitable Lyapunov functions are formulated to analyze the global asymptotic stability of both the disease-free and endemic equilibria. The model is numerically solved using the Grünwald–Letnikov-based nonstandard finite difference method, and simulations assess how the memory index and preventive strategies influence disease propagation. The results reveal critical factors governing TYLCV transmission and suggest effective intervention measures to guide sustainable crop protection policies. Full article

This paper presents a comprehensive strategy for addressing tracking and disturbance rejection for both lumped and distributed parameter systems, focusing on infinite-dimensional input and output spaces. Building on the geometric theory of regulation, the proposed methodology employs a cascade algorithm coupled with Tikhonov regularization to derive control laws that improve tracking accuracy iteratively. Unlike traditional optimal control approaches, the framework minimizes the limsup in time of the tracking error norm, rather than with respect to a quadratic cost function. It is important to note that this work also includes applicability to over- and under-determined systems. We provide theoretical insights, detailed algorithmic formulations, and numerical simulations to demonstrate the effectiveness and generality of the method. Results indicate that the cascade controls asymptotically approximate the classical optimal control solutions, with limitations addressed through rigorous error analysis. Applications include diverse scenarios with both finite and infinite-dimensional input and output spaces, showcasing the versatility of the approach. Full article

The non-stationary heat problem of friction for two homogeneous layers with imperfect thermal contact and convective heat exchange on the free surfaces is considered. Assuming a constant specific power of friction, an exact solution of the formulated problem is obtained using the Laplace integral transform. The solution is verified by checking the fulfillment of the boundary and initial conditions both in the transform space as well as in the space of the original. Particular solutions are also derived for some specific cases, namely, the perfect thermal contact of friction at large values of the contact heat transfer coefficient and the asymptotic solution at the initial time moments of the heating process. On the basis of developed solutions, numerical analysis was performed in dimensionless form. The influence of the thermal contact conductance, the convective cooling intensity, and the relative layer thickness on the temperature field is investigated. It was established that for Biot number $Bi\ge 50$ yields nearly equal surface temperatures. Full article

This paper presents a robust and reliable voltage regulation method in DC–DC converters, for which a multiloop control strategy is developed and analyzed for a boost converter. The proposed control scheme consists of an inner current loop and an outer voltage loop, both systematically designed using the control Lyapunov function (CLF) methodology. The main contributions of this work are (1) the formulation of a control structure capable of maintaining performance under variations in load, reference voltage, and input voltage; (2) the theoretical demonstration of global asymptotic stability of the closed-loop system in the Lyapunov sense; and (3) the experimental validation of the proposed controller on a physical DC–DC boost converter, confirming its effectiveness. The results support the advancement of high-efficiency nonlinear control methods for power electronics applications. Furthermore, the experimental findings reinforce the practical relevance and real-world applicability of the proposed approach. Full article

This research examines the Lyapunov-based criterion for global asymptotic stability of Bidirectional Associative Memory (BAM) neural networks that have mixed-interval time-varying delays. Using a second-order reciprocally convex approach, this paper introduces a novel stability criterion for BAM neural networks with time delays. The literature has recently incorporated a few triple integral expressions in the Lyapunov–Krasovskii functional to lessen conservatism in the analysis of system stability with interval time-varying delays using a second-order reciprocally convex combination strategy. This research work establishes the negative definiteness of the Lyapunov–Krasovskii functional derivative and is formulated using Linear Matrix Inequalities (LMIs). The effectiveness of the proposed result is demonstrated through numerical examples. Full article

In addition to products with a single component, this study examines products composed of multiple components whose lifetimes follow a one-parameter exponential distribution. An overall lifetime performance index is developed to assess products under the progressive type I interval censoring scheme. This study establishes the relationship between the overall and individual lifetime performance indices and derives the corresponding maximum likelihood estimators along with their asymptotic distributions. Based on the asymptotic distributions, the lower confidence bounds for all indices are also established. Furthermore, a hypothesis testing procedure is formulated to evaluate whether the overall lifetime performance index achieves the specified target level, utilizing the maximum likelihood estimator as the test statistic under a progressive type I interval censored sample. Moreover, a power analysis is carried out, and two numerical examples are presented to demonstrate the practical implementation for the overall lifetime performance index. This research can be applied to the fields of life testing and reliability analysis. Full article

This study investigates the geometry of osculating type-2 ruled surfaces in Minkowski 3-space ${\mathbf{E}}_1^3$, formulated through the Type-2 Bishop frame associated with a spacelike curve whose principal normal is timelike and binormal is spacelike. Using the hyperbolic transformation linking the Frenet–Serret and Bishop frames, we analyze how the Bishop curvatures ${\zeta }_1$ and ${\zeta }_2$ affect the geometric behavior and formation of such surfaces. Explicit criteria are derived for cylindrical, developable, and minimal configurations, together with analytical expressions for Gaussian and mean curvatures. We also determine the conditions under which the base curve behaves as a geodesic, asymptotic line, or line of curvature. Several illustrative examples in Minkowski 3-space are provided to visualize the geometric influence of ${\zeta }_1$ and ${\zeta }_2$ on flatness, minimality, and developability. Overall, the Type-2 Bishop frame offers a smooth and effective framework for characterizing Lorentzian geometry and symmetry of osculating ruled surfaces, extending classical Euclidean results to the Minkowski setting. Full article

Pinning control is a key strategy for stabilizing complex networks through a limited set of nodes. However, determining the optimal number and location of pinned nodes under dynamic and structural constraints remains a computational challenge. This work proposes an improved version of the Phymastichus–Hypothenemus Algorithm—Minimized and Determinated (PHA-MD) to solve multi-constraint, hybrid optimization problems in pinning control without requiring a predefined number of control nodes. Inspired by the parasitic behavior of Phymastichus coffea on Hypothenemus hampei, the algorithm models each agent as a parasitoid capable of propagating influence across a network, inheriting node importance and dynamically expanding search dimensions through its “offspring.” Unlike its original formulation, PHA-MD integrates variable-length encoding and V-stability assessment to autonomously identify a minimal yet effective pinning set. The method was evaluated on benchmark network topologies and compared against state-of-the-art heuristic algorithms. The results show that PHA-MD consistently achieves asymptotic stability using fewer pinned nodes while maintaining energy efficiency and convergence robustness. These findings highlight the potential of biologically inspired, dimension-adaptive algorithms in solving high-dimensional, combinatorial control problems in complex dynamical systems. Full article