Networked Turing patterns often manifest as groups of nodes distributed on either side of the homogeneous equilibrium, exhibiting high and low density. These pattern formations are significantly influenced by network topological characteristics, such as the average degree. However, the impact of clustering on them remains inadequately understood. Here, we investigate the relationship between clustering and networked Turing patterns using classical prey–predator models. Our findings reveal that when nodes of high and low density are completely distributed on both sides of the homogeneous equilibrium, there is a linear decay in Turing patterns as global clustering coefficients increase, given a fixed node size and average degree; otherwise, this linear decay may not always hold due to the presence of high-density nodes considered as low-density nodes. This discovery provides a qualitative assessment of how clustering coefficients impact the formation of Turing patterns and may contribute to understanding why using refuges in ecosystems could enhance the stability of prey–predator systems. The results link network topological structures with the stability of prey–predator systems, offering new insights into predicting and controlling pattern formations in real-world systems from a network perspective.

Global warming weakened the summer monsoon and increased the evaporation, leading to more contribution of local evaporation moisture to the local precipitation for the monsoon areas. However, the descriptions of the contribution of the local moisture to the total precipitation and its characteristics have not been known very well. In this paper, taking the middle and lower Reaches of the Yangtze River (MLRYR) as a case and using the precipitation recycling process model, we analyzed the characteristics of the contribution of the local moisture to the total precipitation and the possible reasons. The results show that: the seasonal difference in precipitation recycling rates is obvious, the precipitation recycling rates in spring and summer are small (18.30% and 19.30%), the maximum in autumn is 30.50%, and the precipitation recycling rates in all seasons except summer show a significant upward trend (about 1.70%/10a). Additionally, the water vapor input into MLRYR from four boundaries significantly reduced except for the eastern boundary, and the water vapor contribution from the South and East borders is in summer, and the water vapor contribution from the North and West borders is in autumn, winter and spring. We suggest that the model of the precipitation recycling rate is important to evaluate the contribution of different water vapor sources, and help to further improve the ability of river water prediction in flood season.

Brucellosis remains a persistent public health concern in Inner Mongolia, exhibiting complex spatiotemporal transmission, pronounced periodicity, and strong nonlinear dynamics. To address these challenges, a novel hybrid modeling framework—kernelized Hankel dynamic mode decomposition with sparsity promotion- long short-term memory (KHDMDsp-LSTM) —is proposed for analysis and prediction of epidemic dynamics. The framework’s core innovation is the KHDMDsp, which linearizes nonlinear epidemic processes by embedding low-dimensional system states into a high-dimensional feature space via a hybrid Mercer kernel, enabling extraction of diverse dynamical modes. Kernel parameters are adaptively optimized using Bayesian optimization, and an elastic net regularization strategy promotes sparsity and interpretable mode selection. An integrated LSTM network captures nonlinear temporal dependencies across multiple cities, enhancing long-term prediction. Applied to 11 years of monthly brucellosis data from 12 cities, the framework reconstructs and predicts epidemic dynamics with high fidelity, revealing stable, gradually decaying transmission concentrated in central and eastern Inner Mongolia. Compared with baseline models, KHDMDsp-LSTM demonstrates superior reconstruction and long-horizon prediction, highlighting the potential of combining kernel-based Koopman spectral analysis with deep learning as a robust, data-driven approach for infectious disease modeling and prediction.