The technogenic impact is least felt in specially protected areas whose task is to preserve rare species of animals and plants. Population dynamics is investigated effectively using mathematical models to explore various scenarios of interaction and development of populations, as well as assess the impact of the environment on the spatial-temporal dynamics of biological communities. The paper considers a non-linear model of a protected population, a feature of which is the presence of a bilocal area and the exchange of individuals between its parts. It is a system of nonlinear parabolic partial differential equations that describes the dependence of migration flows on the uneven distribution of individuals on a heterogeneous area with a generalized resource. The influence of the generalized resource on the distribution of the density of parts of a population is investigated using a computational experiment. A specific feature of the model is the presence of a variable cross-diffusion coefficient, which makes it possible to describe the process of excessive concentration of individuals in the most favorable places in terms of resource availability, as a result of which individuals of the population are dispersed in search of a new resource source. The simulation results can be used in the determination of volume of fishing of populations on the unprotected part of the area, the organization of feeding points in a protected part.
One of the methods for protecting the environment and conserving species biodiversity is the creation of protected areas, the task of which is to conserve rare species of animals and plants. The dynamics of populations can be studied quite effectively with the mathematical models. Modeling allows to study all possible scenarios of interaction and development of populations, to evaluate the influence of the environment on the spatial-temporal dynamics of biological communities. The paper considers a non-linear model of a protected population, the feature of which is the presence of a bilocal range and the exchange of species between its parts. It is a system of nonlinear parabolic partial differential equations that describes the dependence of migration flows on the uneven distribution of species in an area with a generalized resource. A complex of programs was coded in Python programming language for numerical study of diffusion models and visualization of the results obtained. Numerical simulation results of cross-diffusion effects and influence of generalized resource are analyzed in detail. The obtained results of research can be used for studying the processes in the protected population, for assessing the size of the protected areas being created, determining the conditions of population degeneration and recommendations for their stable existence.
The paper discusses the impact of allocation of resource reserves for the development of mineral deposits on protected populations. The main method of assessing this effect is mathematical modeling. The results of the study were obtained using a model based on two parabolic partial differential equations (diffusion equations). The equations describe the dynamics of a population in a bilocal habitat, when the boundary of the protected area divides the area into two parts–protected and unprotected. At the same time, the species are free to pass from one part of the habitat to another. The model also takes into account the diffusion movement of species across the habitat and cross-diffusion, which means both the competition of species for available resources and their possible coexistence. Numerical calculations demonstrate that with a proper assessment of the impact on the natural potential of the reserve, it is possible to maintain stable densities of protected populations in both parts of the habitat, but at a slightly lower level. The case of high man-made loads on protected populations leading to their degeneration is also considered. The work shows that the presence of a sufficient food resource has a beneficial effect on the density of the protected and unprotected parts of the population.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.