The analysis of the dynamical system arising from Gray — Scott model

The Gray — Scott system used as a model of three-component autocatalytic reaction X + 2Y → Y, Y → Z, demonstrates the complex behavior and was studied in a number of papers. In this work we refine the known results of the bifurcation analysis of the Gray — Scott system and show them by diagram in parameter space. In addition we construct localizing sets for compact invariant sets of the system, i.e. the sets in the phase space containing all compact invariant sets of the system.