On the existence of oscillatory solutions in the Weisbuch-Salomon-Atlan model for the Belousov-Zhabotinskij reaction

Valter Šeda

Aplikace matematiky (1978)

  • Volume: 23, Issue: 4, page 280-294
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Šeda, Valter. "On the existence of oscillatory solutions in the Weisbuch-Salomon-Atlan model for the Belousov-Zhabotinskij reaction." Aplikace matematiky 23.4 (1978): 280-294. <http://eudml.org/doc/15057>.

@article{Šeda1978,
abstract = {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.},
author = {Šeda, Valter},
journal = {Aplikace matematiky},
keywords = {oscillatory solutions; oscillating oxidation reaction; stability properties; periodic solution; exponential asymptotically stable; generalized Volterra equation; conditionally stable; Oscillatory Solutions; Oscillating Oxidation Reaction; Stability Properties; Periodic Solution; Exponential Asymptotically Stable; Generalized Volterra Equation; Conditionally Stable},
language = {eng},
number = {4},
pages = {280-294},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the existence of oscillatory solutions in the Weisbuch-Salomon-Atlan model for the Belousov-Zhabotinskij reaction},
url = {http://eudml.org/doc/15057},
volume = {23},
year = {1978},
}

TY - JOUR
AU - Šeda, Valter
TI - On the existence of oscillatory solutions in the Weisbuch-Salomon-Atlan model for the Belousov-Zhabotinskij reaction
JO - Aplikace matematiky
PY - 1978
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 23
IS - 4
SP - 280
EP - 294
AB - 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.
LA - eng
KW - oscillatory solutions; oscillating oxidation reaction; stability properties; periodic solution; exponential asymptotically stable; generalized Volterra equation; conditionally stable; Oscillatory Solutions; Oscillating Oxidation Reaction; Stability Properties; Periodic Solution; Exponential Asymptotically Stable; Generalized Volterra Equation; Conditionally Stable
UR - http://eudml.org/doc/15057
ER -

References

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  1. E. A. Coddington N. Levison, Theory of Ordinary Differential Equations, McGraw Hill Book Co., Inc., New York-Toronto-London 1955. (1955) MR0069338
  2. J. Cronin, 10.1016/0022-0396(75)90015-7, J. Differential Equations 19 (1975), 21-35. (1975) Zbl0278.34033MR0397090DOI10.1016/0022-0396(75)90015-7
  3. P. Hartman, Ordinary Differential Equations, (Russian Translation), Izdat. Mir, Moskva 1970. (1970) Zbl0214.09101MR0352574
  4. I. D. Hsū, 10.1016/0022-0396(76)90116-9, J. Differential Equations 20 (1976), 399-403. (1976) MR0457858DOI10.1016/0022-0396(76)90116-9
  5. H. W. Knobloch F. Kappel, Gewöhnliche Differentialgleichungen, B. G. Teubner, Stuttgart, 1974. (1974) MR0591708
  6. Л. С. Понтрягин, Обыкновенные диференциальные уравнения, Издат. Наука, Москва 1970. (1970) Zbl1107.83313
  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. (1975) 

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