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

Aplikace matematiky (1978)

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

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topŠeda, 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

top- E. A. Coddington N. Levison, Theory of Ordinary Differential Equations, McGraw Hill Book Co., Inc., New York-Toronto-London 1955. (1955) MR0069338
- 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
- P. Hartman, Ordinary Differential Equations, (Russian Translation), Izdat. Mir, Moskva 1970. (1970) Zbl0214.09101MR0352574
- 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
- H. W. Knobloch F. Kappel, Gewöhnliche Differentialgleichungen, B. G. Teubner, Stuttgart, 1974. (1974) MR0591708
- Л. С. Понтрягин, Обыкновенные диференциальные уравнения, Издат. Наука, Москва 1970. (1970) Zbl1107.83313
- 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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