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Dynamics of a system of nonlinear differential equations

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Abstract

This is a qualitative analysis of a system of two nonlinear ordinary differential equations which arises in modeling the self-oscillations of the rate of heterogeneous catalytic reaction. The kinetic model under study accounts for the influence of the reaction environment on the catalyst; namely, we consider the reaction rate constant to be an exponential function of the surface concentration of oxygen with an exponent μ. We study the necessary and sufficient conditions for the existence of periodic solutions of differential equations as depending on μ. We formulate some sufficient conditions for all trajectories to converge to a steady state and study global behavior of the stable manifolds of singular saddle points.

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References

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    G. A. Chumakov

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  1. G. A. Chumakov
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Correspondence to G. A. Chumakov.

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__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 5, pp. 1180–1195, September–October, 2007.

Original Russian Text Copyright © 2007 Chumakov G. A.

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Chumakov, G.A. Dynamics of a system of nonlinear differential equations. Sib Math J 48, 949–960 (2007). https://doi.org/10.1007/s11202-007-0098-x

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  • DOI: https://doi.org/10.1007/s11202-007-0098-x

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