The interaction of predators and prey is simulated in a one-dimensional habitat. The model under consideration is formulated as a system of nonlinear parabolic equations with spatial heterogeneity of resources and species. Dynamics is described using reaction-diffusion-advection system. In addition to diffusion, the model assumes taxis forpredator and prey.The natural growth of a prey population is determined by a logistic type of law and the spatial resource function, as well as by the decrease due to the presence of a predator. The increase in predator population density due to the consumption of prey is given by the multiplicative terms, and natural mortality is also taken into account. A numerical study of the influence of directed migration on the formation of population structures and the occupancy rate of the habitat has been carried out. The study found that there are optimal values of the migration parameters at which a distribution of populations of predators and preys with the highest average density is observed.Numerical analysis is based on the finite difference method and staggered grids and allow to follow spatial patterns transformation it time.

Проводится моделирование взаимодействия двух популяций, одна из которых описывает динамику хищников, а другая жертв. Модель записывается в виде системы нелинейных уравнений параболического типа. Помимо случайного распространения по ареалу учитывается направленная миграция, вызванная неравномерностью распределения видов и жизненных условий. Решение системы уравнений проводится методом конечных разностей. Целью работы является исследование влияния миграционных факторов на заполнение популяциями экологических ниш.