Search Results (650)

In this paper, we propose a diffusion-type predator–prey interaction model with harvest and disease in prey, and conduct stability analysis and pattern formation analysis on the model. For the temporal model, the asymptotic stability of each equilibrium is analyzed using the linear stability method, and the conditions for Hopf bifurcation to occur near the positive equilibrium are investigated. The simulation results indicate that an increase in infection force might disrupt the stability of the model, while an increase in harvesting intensity would make the model stable. For the spatiotemporal model, a priori estimate for the positive steady state is obtained for the non-existence of the non-constant positive solution using maximum principle and Harnack inequality. The Leray–Schauder degree theory is used to study the sufficient conditions for the existence of non-constant positive steady states of the model, and pattern formation are achieved through numerical simulations. This indicates that the movement of prey and predators plays an important role in pattern formation, and different diffusions of these species may play essentially different effects. Full article

Conjecture $\mathcal{O}$ (and the Gamma Conjectures), introduced by Galkin, Golyshev, and Iritani stand as pivotal open problems in the quantum cohomology of Fano manifolds, bridging algebraic geometry, mathematical physics, and representation theory. These conjectures aim to decode the structural essence of quantum multiplication by uncovering profound connections between spectral properties of quantum cohomology operators and the underlying geometry of Fano manifolds. Conjecture $\mathcal{O}$ specifically investigates the spectral simplicity and eigenvalue distribution of the operator associated with the first Chern class $c_1$ in quantum cohomology rings, positing that its eigenvalues govern the convergence and asymptotic behavior of quantum products. Full article

We introduce a modern methodology for constructing global analytical approximations of special functions over their entire domains. By integrating the traditional method of matching asymptotic expansions—enhanced with Padé approximants—with differential evolution optimization, a modern machine learning technique, we achieve high-accuracy approximations using elegantly simple expressions. This method transforms non-elementary functions, which lack closed-form expressions and are often defined by integrals or infinite series, into simple analytical forms. This transformation enables deeper qualitative analysis and offers an efficient alternative to existing computational techniques. We demonstrate the effectiveness of our method by deriving an analytical expression for the Fermi gas pressure that has not been previously reported. Additionally, we apply our approach to the one-loop correction in thermal field theory, the synchrotron functions, common Fermi–Dirac integrals, and the error function, showcasing superior range and accuracy over prior studies. Full article

This work investigates fractional stochastic Schrödinger evolution equations in a Hilbert space, incorporating complex potential symmetry and Poisson jumps. We establish the existence of mild solutions via stochastic analysis, semigroup theory, and the Mönch fixed-point theorem. Sufficient conditions for exponential stability are derived, ensuring asymptotic decay. We further explore trajectory controllability, identifying conditions for guiding the system along prescribed paths. A numerical example is provided to validate the theoretical results. Full article

This paper addresses the problem of optimal stabilization for stochastic dynamical systems characterized by Markov switches and concentration points of jumps, which is a scenario not adequately covered by classical stability conditions. Unlike traditional approaches requiring a strictly positive minimal interval between jumps, we allow jump moments to accumulate at a finite point. Utilizing Lyapunov function methods, we derive sufficient conditions for exponential stability in the mean square and asymptotic stability in probability. We provide explicit constructions of Lyapunov functions adapted to scenarios with jump concentration points and develop conditions under which these functions ensure system stability. For linear stochastic differential equations, the stabilization problem is further simplified to solving a system of Riccati-type matrix equations. This work provides essential theoretical foundations and practical methodologies for stabilizing complex stochastic systems that feature concentration points, expanding the applicability of optimal control theory. Full article

In composites, fiber–matrix thermal mismatch induces stress heterogeneity that is beyond the resolution of macroscopic approaches. The asymptotic expansion homogenization method is used to create a multi-scale thermo-mechanical coupling model that predicts the elastic modulus, thermal expansion coefficients, and thermal conductivity of ceramic matrix composites at both the macro- and micro-scales. These predictions are verified to be accurate with a maximum relative error of 9.7% between the measured and predicted values. The multi-scale analysis method is then used to guide the vane’s thermal stress analysis, and a macro–meso–micro multi-scale model is created. The thermal stress distribution and stress magnitudes of the guide vane under a transient high-temperature load are investigated. The results indicate that the temperature and thermal stress distributions of the guide vane under the homogenization and lamination theory models are rather comparable, and the locations of the maximum thermal stress are predicted to be reasonably close to one another. The homogenization model allows for the rapid and accurate prediction of the guide vane’s thermal stress distribution. When compared to the macro-scale stress values, the meso-scale predicted stress levels exhibit excellent accuracy, with an inaccuracy of 11.7%. Micro-scale studies reveal significant stress concentrations at the fiber–matrix interface, which is essential for the macro-scale fatigue and fracture behavior of the guide vane. Full article

Altitude test facilities for aero-engines employ multi-chamber, multi-valve intake systems that require effective decoupling and strong disturbance rejection during transient tests. This paper proposes a coordinated active disturbance rejection control (ADRC) scheme based on external penalty functions. The chamber pressure safety limit is formulated as an inequality-constrained optimization problem, and an exponential penalty together with a gradient based algorithm is designed for dynamic constraint relaxation, with guaranteed global convergence. A coordination term is then integrated into a distributed ADRC framework to yield a multi-valve coordinated ADRC controller, whose asymptotic stability is established via Lyapunov theory. Hardware-in-the-loop simulations using MATLAB/Simulink and a PLC demonstrate that, under ±3 kPa pressure constraints, the maximum engine inlet pressure error is 1.782 kPa (77.1% lower than PID control), and under an 80 kg/s² flow-rate disturbance, valve oscillations decrease from ±27% to ±5%. These results confirm the superior disturbance rejection and decoupling performance of the proposed method. Full article

This work presents a comprehensive mathematical framework for symmetrized neural network operators operating under the paradigm of fractional calculus. By introducing a perturbed hyperbolic tangent activation, we construct a family of localized, symmetric, and positive kernel-like densities, which form the analytical backbone for three classes of multivariate operators: quasi-interpolation, Kantorovich-type, and quadrature-type. A central theoretical contribution is the derivation of the Voronovskaya–Santos–Sales Theorem, which extends classical asymptotic expansions to the fractional domain, providing rigorous error bounds and normalized remainder terms governed by Caputo derivatives. The operators exhibit key properties such as partition of unity, exponential decay, and scaling invariance, which are essential for stable and accurate approximations in high-dimensional settings and systems governed by nonlocal dynamics. The theoretical framework is thoroughly validated through applications in signal processing and fractional fluid dynamics, including the formulation of nonlocal viscous models and fractional Navier–Stokes equations with memory effects. Numerical experiments demonstrate a relative error reduction of up to 92.5% when compared to classical quasi-interpolation operators, with observed convergence rates reaching $\mathcal{O}\left(n^{-1.5}\right)$ under Caputo derivatives, using parameters $\lambda =3.5$, $q=1.8$, and $n=100$. This synergy between neural operator theory, asymptotic analysis, and fractional calculus not only advances the theoretical landscape of function approximation but also provides practical computational tools for addressing complex physical systems characterized by long-range interactions and anomalous diffusion. Full article

This study aims to explore the tracking control challenge in a swarm of multiple nonholonomic wheeled mobile robots (NWMRs) by utilizing a distributed leader–follower strategy grounded in the cascade system theory. Firstly, the kinematic control law is developed for the leader by constructing a sliding surface based on the error tracking model with a virtual reference trajectory. Secondly, a communication topology with the desired formation pattern is modeled for the multiple robots by using the graph theory. Further, in the leader–follower NWMR system, each follower lacks direct access to the leader’s information. Therefore, a novel distributed-based controller by PD-based controller for the follower is developed, enabling each follower to obtain the leader’s information. Thirdly, for each case, we give a further analysis of the closed-loop system to guarantee uniform global asymptotic stability with the conditions based on the cascade system theory. Finally, the trajectory tracking performance of the proposed controllers for the NWMR system is illustrated through simulation results. The leader robot achieved a low RMSE of 1.6572 (Robot 1), indicating accurate trajectory tracking. Follower robots showed RMSEs of 2.6425 (Robot 2), 3.0132 (Robot 3), and 4.2132 (Robot 3), reflecting minor variations due to the distributed control strategy and local disturbances. Full article

In this paper, we study the beamforming design for multiple-input multiple-output (MIMO) ISAC systems, with the weighted mutual information (MI) comprising sensing and communication perspectives adopted as the performance metric. In particular, the weighted sum of the communication mutual information and the sensing mutual information is shown to asymptotically converge to a deterministic limit when the number of transmitting and receiving antennas grow to infinity. This deterministic limit is derived by utilizing the operator-valued free probability theory. Subsequently, an efficient projected gradient ascent (PGA) algorithm is proposed to optimize the transmit beamforming matrix with the aim of maximizing the weighted asymptotic MI. Numerical results validate that the derived closed-form expression matches well with the Monte Carlo simulation results and the proposed optimization algorithm is able to improve the weighted asymptotic MI significantly. We also illustrate the trade-off between asymptotic sensing and asymptotic communication MI. Full article

Aimed at dealing with the problems of high reliability solution cost and low solution accuracy under random excitation, especially Gaussian white noise excitation, this paper proposes a probability density evolution and reliability analysis method for nonlinear gear transmission systems under Gaussian white noise excitation based on the path integration method. This method constructs an efficient probability density evolution framework by combining the path integration method, the Chapman–Kolmogorov equation, and the Laplace asymptotic expansion method. Based on Rice’s theory and combined with the adaptive Gauss–Legendre integration method, the transient and cumulative reliability of the system are path integration method calculated. The research results show that in the periodic response state, Gaussian white noise leads to the diffusion of probability density and peak attenuation, and the system reliability presents a two-stage attenuation characteristic. In the chaotic response state, the intrinsic dynamic instability of the system dominates the evolution of the probability density, and the reliability decreases more sharply. Verified by Monte Carlo simulation, the method proposed in this paper significantly outperforms the traditional methods in both computational efficiency and accuracy. The research reveals the coupling effect of Gaussian white noise random excitation and nonlinear dynamics, clarifies the differences in failure mechanisms of gear systems in periodic and chaotic states, and provides a theoretical basis for the dynamic reliability design and life prediction of nonlinear gear transmission systems. Full article

In this paper, we focus on mean-field stochastic differential equations driven by G-Brownian motion (G-MFSDEs for short) with a drift coefficient satisfying the local one-sided Lipschitz condition with respect to the state variable and the global Lipschitz condition with respect to the law. We are concerned with the well-posedness and the numerical approximation of the G-MFSDE. Probability uncertainty leads the resulting expectation usually to be the G-expectation, which means that we cannot apply the numerical approximation for McKean–Vlasov equations to G-MFSDEs directly. To numerically approximate the G-MFSDE, with the help of G-expectation theory, we use the sample average value to represent the law and establish the interacting particle system whose mean square limit is the G-MFSDE. After this, we introduce the modified stochastic theta method to approximate the interacting particle system and study its strong convergence and asymptotic mean square stability. Finally, we present an example to verify our theoretical results. Full article

This paper introduces a novel field-oriented control (FOC) strategy for an open-end stator three-phase winding induction motor (OEW-TP-IM) using dual space vector modulation-pulse width modulation (SVM-PWM) inverters. This configuration reduces common mode voltage at the motor’s terminals, enhancing efficiency and reliability. The study presents a backstepping control approach combined with a mean value theorem (MVT)-based observer to improve control accuracy and stability. Stability analysis of the backstepping controller for key control loops, including flux, speed, and currents, is conducted, achieving asymptotic stability as confirmed through Lyapunov’s methods. An advanced observer using sector nonlinearity (SNL) and time-varying parameters from convex theory is developed to manage state observer error dynamics effectively. Stability conditions, defined as linear matrix inequalities (LMIs), are solved using MATLAB R2016b to optimize the observer’s estimator gains. This approach simplifies system complexity by measuring only two line currents, enhancing responsiveness. Comprehensive simulations validate the system’s performance under various conditions, confirming its robustness and effectiveness. This strategy improves the operational dynamics of OEW-TP-IM machine and offers potential for broad industrial applications requiring precise and reliable motor control. Full article

The aim of this work is to develop a discrete-time control algorithm that allows the attitude angle of a satellite with an attached solar panel to track a prescribed periodically changing reference signal with zero asymptotic error. Using the concept of the general regulation theory for the state space setup, combined with a time discretization procedure based on the Cayley–Tustin transformation, we derive an error feedback controller. In our control analysis, we prove and explore several system-theoretic properties that are preserved under this continuous-to-discrete time transformation. The obtained discrete-time controller is then applied as a digital control system, demonstrating zero asymptotic tracking error. The theoretical results are tested on a numerical example and computations are performed within the MATLAB R2024b environment, confirming the highly useful nature of the developed approach. The controller also shows some robustness with respect to parametric uncertainty in the satellite model. Full article

Recent observations suggest that General Relativity (GR) faces challenges in fully explaining phenomena in regimes of strong gravitational fields. A promising alternative is the $f\left(R\right)$ theory of gravity, where R denotes the Ricci scalar. This modified theory aims to address the limitations observed in standard GR. In this study, we derive a black hole (BH) solution without introducing nonlinear electromagnetic fields or imposing specific constraints on R or the functional form of $f\left(R\right)$ gravity. The BH solution obtained here is different from the classical Schwarzschild solution in GR and, under certain conditions, reduces to the Schwarzschild (A)dS solution. This BH is characterized by the gravitational mass of the system and an additional parameter, which distinguishes it from GR BHs, particularly in the asymptotic regime. We show that the curvature invariants of this solution remain well defined at both small and large values of r. Furthermore, we analyze their thermodynamic properties, demonstrating consistency with established principles such as Hawking radiation, entropy, and quasi-local energy. This analysis supports their viability as alternative models to classical GR BHs. Full article