Mathematical Methods in the Applied Sciences最新文献

To investigate the inner synchronization of stochastic complex-valued coupled networks, a hybrid control method named aperiodically intermittent discrete observation control (AIDOC) is proposed in the sense of average, which combines the merits of discrete time state observation control and aperiodically intermittent control. By using the average technique, the minimum control ratio condition, quasi-periodicity condition is not required, which makes our results more general and less conservative. Moreover, by employing the Lyapunov method and graph theory, some sufficient conditions are given to guarantee the realization of the synchronization. Then, the inner synchronization of stochastic complex-valued coupled oscillators (SCCOs) is considered via AIDOC. Eventually, several numerical simulations are given to testify the effectiveness of the results developed.

This paper introduces a novel meshless method based on polynomials for solving a class of integro-differential equations with tempered fractional singular kernels. Our method employs a least-squares partition of unity framework based on local polynomial approximations in spatial discretization. To enhance numerical stability, the global approximation is constructed by blending local approximations over overlapping subdomains through the use of partition of unity weight functions. For temporal discretization, two convolution quadrature rules are employed for the tempered fractional operator, leading to the development of two time-stepping schemes. The proposed method is applied to some test problems defined on rectangular, elliptical, and irregular domains. The numerical results confirm the accuracy, efficiency, and robustness of the proposed method in handling various geometries.

The third fractional 3D Wazwaz–Benjamin–Bona–Mahony (WBBM) equation is examined in this paper, along with new waveforms and various analyses. This is important for understanding how waves move in plasma physics, shallow water, and nonlinear optics. We use a Galilean transformation to obtain the research output of this model. The planner dynamic system of the equation is also constructed, and all possible phase portrait analyses are described, including bifurcation and chaos. We observed chaotic, periodic, and quasi-periodic behaviors by introducing a perturbed term for various parameter values. This study talks about multistability analysis, sensitivity analysis, and exact traveling wave solutions of the governing model. Fractal dimension, strange attractor, recurrence plot, power spectrum, return map, and Lyapunov exponent (LE) are some of the graphs that show how the model works. Additionally, this research work employs the unified solver technique to yield diverse solitary-wave outcomes. We visually display the derived outcomes in 2D and 3D plots. We can conclude that these findings provide a solid foundation for further investigation and are valuable, useful, and reliable for dealing with future complex nonlinear problems. The approach employed in this work demonstrates a high level of reliability, robustness, and efficiency, making it suitable for addressing a vast area of nonlinear partial differential equations (NLPDEs) that have not been studied in any other research.

This article mainly discusses $��p�$th moment exponential stability for impulsive stochastic dynamical systems with unbounded delay. By utilizing the improved Lyapunov–Razumikhin approach together with the mode-dependent average dwell time method, some novel criteria are obtained from the perspective of impulsive perturbation and impulsive control, which specifically provide the intrinsic connection among current state, unbounded delay and multiple impulses. Compared with some existing works, it should be highlighted that our results do not require the steady state behavior of both discrete system and continuous dynamical system. Finally, two numerical examples are presented to demonstrate the validity and the distinctiveness of derived results.

This paper extends the framework of classical eco-evolutionary game theory by establishing an asymmetric two-community resource coupling model. By defining distinct community types, we simulate the asymmetry in environmental resource management and consumption across communities. Under the assumption that only one community is responsible for environmental resources, we theoretically and numerically analyze the equilibria and their stability. The model exhibits rich dynamic behaviors, including Hopf bifurcations and a heteroclinic network composed of six heteroclinic cycles within the system. To prevent resource collapse, we derive the maximum resource consumption threshold for the irresponsible community. The results show that the conditions for system stability in single-community models no longer apply in multicommunity systems, and excessive cross-community interactions may cause systemic risks. This work extends existing research and provides a new theoretical perspective for understanding the asymmetric evolution of multicommunity resource coupling.

The pneumonia caused by coronavirus infection seriously threatens the lives and health of the people and is a war without fire. The paper considers the COVID-19 model with susceptible, latent, asymptomatic, symptomatic, and rehabilitative stages. First, we study the local stability of boundary equilibrium points for deterministic systems. Then, the model is dimensionally reduced by a limit set, and the method of Lyapunov functions is used to prove that the endemic equilibrium point is locally asymptotically stable for the dimensionally reduced model. For stochastic systems with Ornstein–Uhlenbeck processes, we first prove the existence and uniqueness of positive solution. In addition, in-depth research was conducted on the persistence and extinction of the disease. And the density function near the positive equilibrium point is described in detail. Finally, some numerical simulations help us verify the above conclusions.

This paper introduces novel error bounds for Weddle's quadrature rule—a sixth-degree Newton–Cotes numerical integration method—using a new kernel. Unlike classical approaches requiring six-time differentiability, our results leverage twice-differentiable convex functions to derive tighter error estimates, significantly broadening applicability. We establish a key identity involving the second derivative and use it to prove inequalities for diverse function classes, including convexity, boundedness, and Lipschitz continuity. By using novel identity, we obtained refined bounds based on Hölder's, power-mean, and Young's inequalities, improving upon prior work. Applications to special functions ($��q�$-digamma and Bessel) and composite quadrature rules demonstrate practical utility. Computational analysis and graphical presentations confirm the effectiveness of our results. Furthermore, we quantify the sensitivity of these bounds to integration-interval width, revealing a precise quadratic dependence on ($��{�z�}_{�2�}�-�{�z�}_{�1�}�$) that guides partition-size selection in practice.

Quantum calculus extends classical calculus through the inclusion of a parameter $��q�$, thereby broadening the conceptual framework for analysis. The present study provides novel variants of Boole's formula-type inequalities for $��q�$-differentiable convex functions via first deriving an essential quantum-integral identity. The derived results enhance classical findings and highlight the distinctive properties of convex functions in quantum calculus. The application to quadrature formula, special means of real numbers, and the Mittag-Leffler function demonstrates the practical relevance of our newly derived results. Numerical and graphical examples further verify the accuracy and effectiveness of the presented inequalities, indicating their suitability for real-world circumstances. The present work strengthens the theoretical understanding of Boole's formula-type inequalities in quantum and classical domains and offers interesting possibilities for future research in numerical analysis.