Huancas Fernando, Coronel Anibal, Lozada Esperanza, Torres Jorge
Departamento de Matemática, Facultad de Ciencias Naturales, Matemáticas y del Medio Ambiente, Universidad Tecnológica Metropolitana, Ñuñoa, Santiago 7750000, Chile.
Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán 3780000, Chile.
Biology (Basel). 2025 Sep 22;14(9):1308. doi: 10.3390/biology14091308.
In this paper, we develop a systematic review of the existing literature on the mathematical modeling of several aspects of pollinators. We selected the MathSciNet and Wos databases and performed a search for the words "pollinator" and "mathematical model". This search yielded a total of 236 records. After a detailed screening process, we retained 107 publications deemed most relevant to the topic of mathematical modeling in pollinator systems. We conducted a bibliometric analysis and categorized the studies based on the mathematical approaches used as the central tool in the mathematical modeling and analysis. The mathematical theories used to obtain the mathematical models were ordinary differential equations, partial differential equations, graph theory, difference equations, delay differential equations, stochastic equations, numerical methods, and other types of theories, like fractional order differential equations. Meanwhile, the topics were positive bounded solutions, equilibrium and stability analysis, bifurcation analysis, optimal control, and numerical analysis. We summarized the research findings and identified some challenges that could inform the direction of future research, highlighting areas that will aid in the development of future research.
在本文中，我们对现有关于传粉者若干方面数学建模的文献进行了系统综述。我们选择了MathSciNet和Wos数据库，并搜索了“传粉者”和“数学模型”这两个词。此次搜索共得到236条记录。经过详细的筛选过程，我们保留了107篇被认为与传粉者系统数学建模主题最相关的出版物。我们进行了文献计量分析，并根据在数学建模和分析中用作核心工具的数学方法对这些研究进行了分类。用于获得数学模型的数学理论有常微分方程、偏微分方程、图论、差分方程、延迟微分方程、随机方程、数值方法以及其他类型的理论，如分数阶微分方程。同时，主题包括正有界解、平衡与稳定性分析、分岔分析、最优控制和数值分析。我们总结了研究结果，并确定了一些可为未来研究方向提供参考的挑战，突出了有助于未来研究发展的领域。
