The aim of this work is to determine the conditions under which multistability is possible in system of three competing species described by reaction–diffusion–advection equations.

Methods. Using the theory of cosymmetry and the concept of ideal free distribution, relations are established for the coefficients of local interaction, diffusion and directed migration, under which continuous families of solutions are possible. Compact scheme of the finite difference method is used to discretize the problem of species distribution on one-dimensional spatial area with periodicity conditions.

Results. Conditions for parameters are found, under which stationary solutions proportional to the resource are obtained, corresponding to the ideal free distribution (IFD). The conditions under which two-parameter families of stationary distributions exist are studied. For parameters corresponding to IFD, family of periodic regimes is obtained in computational experiment.

Conclusion. The obtained results demonstrate variants of multistability of species in resource-heterogeneous area and will further serve as a basis for the analysis of systems of interacting populations.