Mathematical model for conservation of biological diversity

Abstract

This article discusses a mathematical model designed to analyze the dynamics of populations and their interactions in an ecosystem. The model is based on a system of Lotka-Volterra differential equations, extended to take into account additional environmental factors such as climate change, natural resource use, and the impact of anthropogenic factors. Creating a mathematical model for the conservation of biological diversity is a complex task that requires taking into account many factors and interactions between them. The model includes coefficients describing population growth rates, their interactions, and diffusion, which takes into account the spatial distribution of species. The study demonstrates the application of the model using the example of an ecosystem in the dry regions of Uzbekistan, where interactions between plant populations and parasitic insects are examined. The modeling results make it possible to predict changes in the ecosystem in response to various climatic and anthropogenic impacts, as well as to develop adaptation strategies for the conservation of biodiversity. The proposed model is a powerful tool for environmental research, allowing not only to understand current processes in ecosystems, but also to predict their future state. Thus, the model contributes to the development of effective measures for environmental protection and sustainable management of natural resources.