Abstract. Based on the differential equations of diffusion-advection-reaction, a mathematical model of the "predator-prey" with an ideal free distribution on a heterogeneous two-dimensional ring-shaped habitat is described. A simple mathematical description of an annular habitat with an uneven distribution of a generalized resource is presented. It has been established that in the presence of diffusion and multifactorial taxis, the predator-prey system can have a stationary solution corresponding to the coexistence of two species. Stability conditions are found, the violation of which leads to a transition either to a solution without a predator or to an oscillatory regime. The form of the functions of directed migration and the relationship between the coefficients of the system, when fulfilled, the  ideal free distribution is realized, are given. Studies have been conducted on the stability of the stationary solution and the deviation of species distributions from the  ideal free distribution with small variations in parameters.