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Mathematical aspects of modeling self-oscillations of the heterogeneous catalytic reaction rate. I. (Russian, English) Zbl 1121.34050
Sib. Mat. Zh. 46, No. 5, 1179-1189 (2005); translation in Sib. Math. J. 46, No. 5, 948-956 (2005).
Summary: A theoretical study of a special system of ordinary differential equations is presented. The system models self-oscillations of the reaction rate in a heterogeneous catalytic reaction. The existence periodic solutions of autonomous systems with a small parameter at the leading order derivatives are studied. We show the validity of the quasistationary 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.
MSC:
34C26 Relaxation oscillations for ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
80A32 Chemically reacting flows
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