Mathematical Methods in the Applied Sciences最新文献

This paper addresses the stabilization problem for the Schrödinger equation with dynamic boundary condition of Wentzell type. Under suitable assumption about the damping domain, we demonstrate that sufficiently smooth solutions of the Schrödinger equation decay logarithmically. The proof is based on some frequency estimates with exponential loss on the resolvent operators, which will be solved by establishing an interpolation inequality for a suitable parabolic equation with Wentzell-type boundary condition.

This paper proposes a control approach for achieving practical predefined-time stabilization in a class of nonlinear systems influenced by matched bounded disturbances and unknown nonlinearities. Radial basis function (RBF) neural networks (NNs) are used for function approximation to tackle these uncertainties. By applying Lyapunov stability theory, we show that the proposed time-varying control law and adaptive mechanism ensure the convergence of the system states to a region around the equilibrium within a predefined time, while all closed-loop signals remain bounded. The effectiveness of the approach is validated through simulations on a single-link flexible-joint robotic manipulator.

In this paper, based on Euler–Marryama method and the theory of stochastic processes, considering that changes in crop, pest and natural enemy populations can be affected by environmental white noise during the process of integrated pest management (IPM), the data of biological samples is usually collected in discrete time, and the successive generations of many species in nature are nonoverlapping, a stochastic discrete crop-pest-natural enemy model is established and investigated. Firstly, the stability of the equilibria of deterministic continuous crop-pest-natural enemy model with IPM strategy is analyzed. Secondly, by using Lyapunov function and the theory of stochastic difference equation, sufficient conditions for the asymptotic mean square stability of the linearized stochastic difference equation corresponding to its translational transformation at zero solution are given, thus the stability in probability of the nonlinear stochastic discrete crop-pest-natural enemy model at the pest-extinction equilibrium and positive equilibrium are obtained. Further, numerical simulations are used to confirm the theoretical results. Finally, considering that white noise mainly affects the growth rate and mortality rate of crop, pest and natural enemy populations, an improved stochastic discrete crop-pest-natural enemy model is established to investigate the effects of white noise intensity on population survival, and the results show that weak-intensity noise dose not affect the survival and extinction of the population, however, high-intensity noise may cause extinction in previously persistent populations.

This paper investigates the existence, uniqueness, continuous dependence, and asymptotic behavior of mild solutions for the nonautonomous neutral stochastic functional differential equations involving fractional Brownian motion and state-dependent delay. First, by employing estimates on nonlinear terms and operator theory, the existence, uniqueness, and continuous dependence of solutions for the considered system were established. Subsequently, using the Arzelà–Ascoli theorem, the Schauder fixed-point theorem, and operator-theoretic methods, we analyze the global existence and asymptotic behavior of mild solutions. Moreover, we study the existence of a global forward-attracting set in the mean-square sense. Finally, an illustrative example is provided to demonstrate the applicability of the theoretical results.

In this paper, we propose a class of time-delayed epidemic models for Hepatitis E. Based on the transmission mechanism of Hepatitis E and taken into account factors such as environmental transmission, vaccination, and the latent period delay, a Hepatitis E disease model with time delay is constructed. Through dynamic analysis of the model, the basic reproduction number $��{�ℛ�}_{�0�}�$ and equilibrium points of the model are determined. When $��{�ℛ�}_{�0�}�\le �1�$, the disease-free equilibrium is globally asymptotically stable; when $��{�ℛ�}_{�0�}�>�1�$, the endemic equilibrium is globally asymptotically stable. Numerically, we study the Hepatitis E transmission trends in Shaanxi Province, China. The partial rank correlation coefficient method is employed to analyze the impact of different parameters on the basic reproduction number $��{�ℛ�}_{�0�}�$. Furthermore, some control strategies are provided to prevent Hepatitis E spread in Shaanxi.

This paper is concerned with the well-posedness and existence of weak pullback mean random attractors for a class of reaction–diffusion equations with nonlocal coefficient and nonlinear multiplicative noise. In our problem, the coefficient can be degenerate, and the nonlinearity is not locally Lipschitz on the phase space.

This paper investigates the local exponential synchronization-like control between state-dependent impulsive chaotic neural networks. First, various adequate conditions are theoretically proven to guarantee that the trajectory of every solution for the chaotic neural networks passes through each impulsive surface only once. Second, by designing segmented controllers and aperiodic intermittent controllers, respectively, making use of the comparison principle and linear matrix inequality techniques, this paper establishes adequate conditions for the local exponential synchronization-like control between impulsive chaotic neural networks. Finally, the validity of the proposed results was confirmed by using examples and numerical simulations.

The work covers a nonlocal problem of the Bitsadze-Samarskii type for a degenerate elliptic equation of fractional order in a vertical half-strip $��\Omega �=�\left\{�\right(�x�,�t�)�:�0�<�x�<�1�,�t�>�0�\}�$. This problem connects the value of the sought function on the right boundary with its value at an internal point of the domain. Theorems on the existence and uniqueness of a solution to the problem are proved using the spectral method, with the solution constructed as a series sum over the eigenfunctions of the corresponding one-dimensional spectral problem. The work also studied the spectral properties of a Bitsadze–Samarskii type problem for a second-order ordinary differential equation obtained via the spectral method. Eigenvalues and the corresponding root functions are determined, their completeness and basis properties are proved, and the adjoint problem is analyzed.