| Title:
|
On the existence of oscillatory solutions in the Weisbuch-Salomon-Atlan model for the Belousov-Zhabotinskij reaction (English) |
| Author:
|
Šeda, Valter |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
23 |
| Issue:
|
4 |
| Year:
|
1978 |
| Pages:
|
280-294 |
| Summary lang:
|
English |
| Summary lang:
|
Slovak |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
oscillatory solutions |
| Keyword:
|
oscillating oxidation reaction |
| Keyword:
|
stability properties |
| Keyword:
|
periodic solution |
| Keyword:
|
exponential asymptotically stable |
| Keyword:
|
generalized Volterra equation |
| Keyword:
|
conditionally stable |
| MSC:
|
34C15 |
| MSC:
|
34C25 |
| MSC:
|
34D20 |
| MSC:
|
92A09 |
| idZBL:
|
Zbl 0405.34048 |
| idMR:
|
MR0495430 |
| DOI:
|
10.21136/AM.1978.103753 |
| . |
| Date available:
|
2008-05-20T18:09:52Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103753 |
| . |
| Reference:
|
[1] E. A. Coddington N. Levison: Theory of Ordinary Differential Equations.McGraw Hill Book Co., Inc., New York-Toronto-London 1955. MR 0069338 |
| Reference:
|
[2] J. Cronin: Periodic Solutions in n Dimensions and Volterra Equations.J. Differential Equations 19 (1975), 21-35. Zbl 0278.34033, MR 0397090, 10.1016/0022-0396(75)90015-7 |
| Reference:
|
[3] P. Hartman: Ordinary Differential Equations.(Russian Translation), Izdat. Mir, Moskva 1970. Zbl 0214.09101, MR 0352574 |
| Reference:
|
[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. MR 0457858, 10.1016/0022-0396(76)90116-9 |
| Reference:
|
[5] H. W. Knobloch F. Kappel: Gewöhnliche Differentialgleichungen.B. G. Teubner, Stuttgart, 1974. MR 0591708 |
| Reference:
|
[6] Л. С. Понтрягин: Обыкновенные диференциальные уравнения.Издат. Наука, Москва 1970. Zbl 1107.83313 |
| Reference:
|
[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. 10.1051/jcp/1975720071 |
| . |
