Mathematical and Computational Applications

In this study, a comprehensive analysis of the fixed/preassigned-time synchronization of a class of quaternion-valued BAM (QBAM) neural networks with stochastic and impulsive effects is conducted. Unlike previous analysis methods, our method features a direct analysis approach. First, to clarify the combined impact of impulsive and stochastic phenomena on synchronization behavior, we establish a QBAM neural network system incorporating stochastic and impulsive effects. Notably, differing from prior relevant studies, we assume that the activation function is discontinuous, thereby enhancing the practical relevance of this research. Second, leveraging the quaternion-valued sign function and its properties, we implement impulsive control via the direct analysis method to achieve Fixed/Predefined-Time synchronization of the considered system. Finally, numerical simulations are performed to verify the ability of the theoretical analysis and the proposed control protocol to realize synchronization under impulsive and stochastic effects.

Urban catchments are increasingly vulnerable to hydrologic extremes driven by land-use change and climate variability, challenging the traditional assumption of stationarity. This study develops a computational framework to assess the nonstationary behavior of peak flow, volume, and duration in an urban catchment in the Philippines using 39 years of daily flow records (June 1984–November 2022). Missing observations (~8% of the series) were reconstructed using multiple linear regression (MLR) and artificial neural networks (ANNs) with four predictors: daily rainfall, antecedent rainfall, antecedent flow, and built-up area index. MLR with all predictors yielded the most accurate reconstructions. Nonstationarity was detected using the Mann–Kendall test, Sen slope estimator, Pettitt test, and variance change test. Flood events were extracted using block maxima (BM) and peak-over-threshold (POT) methods. BM-based results showed stationary peak flow and volume, while duration increased by 1.78 h/year. POT analyses revealed nonstationarity across all variables, without significant shifts in variance. These findings demonstrate that methodological choices strongly influence nonstationary detection. The framework underscores the importance of reliable data reconstruction and robust statistical testing for nonstationary analysis of flood events. POT-based approaches more effectively capture evolving trends in peak flow, volume, and duration. These can be used in designing resilient infrastructure and flood risk management in urbanizing catchments.

Advection–diffusion–reaction-type interface models have wide-ranging applications in environmental science, chemical engineering, and biological systems, particularly in modeling pollutant transport in groundwater, reactive flows, and drug diffusion across biological membranes. This paper presents a novel numerical method for the solution of these models. The proposed method integrates the meshless collocation technique with the finite difference method. The temporal derivative is approximated using a finite difference scheme, while spatial derivatives are approximated using radial basis functions. The interface across the fixed boundary is treated with discontinuous diffusion, advection, and reaction coefficients. The proposed numerical scheme is applied to both linear and non-linear models. The Gauss elimination method is used for the linear models, while the quasi-Newton linearization method is employed to address the non-linearity in non-linear cases. The $L_{\infty }$ error is computed for varying numbers of collocation points to assess the method’s accuracy. Furthermore, the performance of the method is compared with the Haar wavelet collocation method and the immersed interface method. Numerical results demonstrate that the proposed approach is more efficient, accurate, and easier to implement than existing methods. The technique is implemented in MATLAB R2024b software.