Mathematical aspects of modeling the self-oscillations of the heterogeneous catalytic reaction rate. I

Theoretical study is presented of a special system of ordinary differential equations. The system is related to the mathematical modeling of self-oscillations of the reaction rate in a heterogeneous catalytic reaction. The periodic solutions of autonomous systems with a small parameter at the leading order derivatives are studied. We show the validity of the quasistationarity principle provided that the velocity of the reacting mixture in the reactor is high. That allows us to decrease the number of variables in the model while keeping the general model properties. A new principle of the generation of relaxation oscillations in the three-dimensional kinetic model with two fast and one slow variables is proposed.