The Kolmogorov model has been applied to many biological and environmental problems. We are particularly interested in one of its variants, that is, a Gauss-type predator–prey model that includes the Allee effect and Holling type-III functional response. Instead of using classic first order differential equations to formulate the model, fractional order differential equations are utilized. The existence and uniqueness of a nonnegative solution as well as the conditions for the existence of equilibrium points are provided. We then investigate the local stability of the three types of equilibrium points by using the linearization method. The conditions for the existence of a Hopf bifurcation at the positive equilibrium are also presented. To further affirm the theoretical results, numerical simulations for the coexistence equilibrium point are carried out.

We present a fractional-order model of two-species facultative mutualism with harvesting. We investigate the stability of the equilibrium points of the model by using the linearization method for noncoexistence of equilibrium points and the Lyapunov direct method for the positive coexistence of an equilibrium point. In addition, we obtain sufficient conditions to ensure the local asymptotic stability and global uniform asymptotic stability for the model. Finally, we provide illustrated numerical examples to verify the stability results obtained in this study.

Ordinary kriging (OK) is a popular interpolation method for its ability to simultaneously minimize error variance and deliver statistically optimal and unbiased predictions. In this work, the adaptive moving window kriging with K-means clustering (AMWKK) technique is developed to improve the estimation obtained from the moving window kriging based on the K-means clustering proposed by Abedini et al. This technique specifically addresses the challenge of selecting appropriate windows for target points located near the borders, which can potentially be the source of errors. The AMWKK algorithm introduces a dynamic clustering approach within the moving window kriging, where each target site sequentially serves as a cluster centroid. The OK is then applied within the cluster encompassing the target point, ensuring localized and adaptive interpolation. The proposed method is compared with ordinary kriging and other moving window kriging variant approaches to estimate Thailand’s mean annual pressure and humidity in 2018. The results indicate superior estimation capabilities of the AMWKK approach in terms of distinct quantitative performance statistics. The advantage of using the AMWKK method for spatial interpolation can be attributed to the fact that it facilitates the automatic tuning of the window size at any estimation point. The algorithm is particularly effective when observations in the same cluster as target points are sparse.

Spatial interpolation of meteorological data can have immense implications on risk management and climate change planning. Kriging with external drift (KED) is a spatial interpolation variant that uses auxiliary information in the estimation of target variables at unobserved locations. However, traditional KED methods with linear trend functions may not be able to capture the complex and non-linear interdependence between target and auxiliary variables, which can lead to an inaccurate estimation. In this work, a novel KED method using least squares support vector regression (LSSVR) is proposed. This machine learning algorithm is employed to construct trend functions regardless of the type of variable interrelations being considered. To evaluate the efficiency of the proposed method (KED with LSSVR) relative to the traditional method (KED with a linear trend function), a systematic simulation study for estimating the monthly mean temperature and pressure in Thailand in 2017 was conducted. The KED with LSSVR is shown to have superior performance over the KED with the linear trend function.

Geostatistical interpolation methods, sometimes referred to as kriging, have been proven effective and efficient for the estimation of target quantity at ungauged sites. The merit of the kriging approach relies heavily on the semivariograms in which the parametric functions are prevalently used. In this work, we explore the semiparametric semivariogram where no close-form semivariogram is required. By additionally enforcing the monotonicity condition in order to suppress the presence of spurious oscillation, a scaling of the nodes of the semiparametric kriging is proposed. To this end, the solar radiation estimates across extensive but unmeasured regions in Thailand using three different semivariogram models are undertaken. A cross validation analysis is carried out in order to justify the performance of each approach. The best results are achieved by the semiparametric model with an improvement of around 7–13% compared to those obtained from the parametric semivariograms.