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oscillatory solutions; oscillating oxidation reaction; stability properties; periodic solution; exponential asymptotically stable; generalized Volterra equation; conditionally stable
The stability properties of solutions of the differential system which represents the considered model for the Belousov - Zhabotinskij reaction are studied in this paper. The existence of oscillatory solutions of this system is proved and a theorem on separation of zero-points of the components of such solutions is established. It is also shown that there exists a periodic solution.
[1] E. A. Coddington N. Levison: Theory of Ordinary Differential Equations. McGraw Hill Book Co., Inc., New York-Toronto-London 1955. MR 0069338
[2] J. Cronin: Periodic Solutions in n Dimensions and Volterra Equations. J. Differential Equations 19 (1975), 21-35. DOI 10.1016/0022-0396(75)90015-7 | MR 0397090 | Zbl 0278.34033
[3] P. Hartman: Ordinary Differential Equations. (Russian Translation), Izdat. Mir, Moskva 1970. MR 0352574 | Zbl 0214.09101
[4] I. D. Hsū: Existence of Periodic Solutions for the Belousov-Zaikin-Zhabotinskij Reaction by a Theorem of Hopf. J. Differential Equations 20 (1976), 399-403. DOI 10.1016/0022-0396(76)90116-9 | MR 0457858
[5] H. W. Knobloch F. Kappel: Gewöhnliche Differentialgleichungen. B. G. Teubner, Stuttgart, 1974. MR 0591708
[6] Л. С. Понтрягин: Обыкновенные диференциальные уравнения. Издат. Наука, Москва 1970. Zbl 1107.83313
[7] G. Weisbuch J. Salomon, H. Atlan: Analyse algébrique de la stabilité d'un système à trois composants tiré de la réaction de Jabotinski. J. de Chimie Physique, 72 (1975), 71 - 77.
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