Dynamics of population kinetics model with cosymmetry

Dynamics of a cosymmetric system of nonlinear parabolic equations is studied to model population kinetics of three interacting species. Finite-difference scheme which preserves a cosymmetry of the underlying problem is developed. Method of computation for continuous family of equilibria is derived. Different scenarios of instability in the model are analyzed as well as evolution of nonstationary regimes and families of steady states.