| Title:
|
Stability of a model for the Belousov-Zhabotinskij reaction (English) |
| Author:
|
Haluška, Vladimír |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1989 |
| Pages:
|
89-104 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the Field-Körös-Noyes' model of the Belousov-Yhabotinskij reaction. By means of the method of the Ljapunov function a sufficient condition is determined that the non-trivial critical point of this model be asymptotically stable with respect to a certain set. (English) |
| Keyword:
|
Field-Körös-Noyes’ model |
| Keyword:
|
Belousov-Zhabotinskij reaction |
| Keyword:
|
Lyapunov function |
| Keyword:
|
equilibrium point |
| Keyword:
|
stability in the large |
| MSC:
|
34D20 |
| MSC:
|
80A30 |
| idZBL:
|
Zbl 0681.34047 |
| idMR:
|
MR0990297 |
| DOI:
|
10.21136/AM.1989.104338 |
| . |
| Date available:
|
2008-05-20T18:36:09Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104338 |
| . |
| Reference:
|
[1] K. Bachratý: On the stability of a model for the Belousov-Zhabotinskij reaction.Acta mathematica Univ. Comen. XLII-XLIII (2983), 225-234. MR 0740754 |
| Reference:
|
[2] R. J. Field R. M. Noyes: Oscillations in chemical systems. IV. Limit cycle behaviour in in a model of a real chemical reaction.J. Chem. Phys. 60 (1974), 1877-1884. 10.1063/1.1681288 |
| Reference:
|
[3] P. Hartman: Ordinary Differential Equations.J. Wiley and Sons, New York-London-Sydney (1964) (Russian translation, Izdat Mir, Moskva, 1970). Zbl 0125.32102, MR 0171038 |
| Reference:
|
[4] I. D. Hsü: Existence of periodic solutions for the Belousov-Zaikin-Zhabotinskij reaction by a theorem of Hopf.J. Differential Equations 20 (1976), 339-403. MR 0457858 |
| Reference:
|
[5] J. La Salle S. Lefschetz: Stability by Liapunov'z Direct method with applications.Academic Press, New York-London (2961) (Russian translation, Izdat. Mir, Moskva, 1964). |
| Reference:
|
[6] J. D. Murray: On a model for temporal oscillations in the Belousov-Zhabotinskij reaction.J. Chem. Phys. 6 (1975), 3610-3613. |
| Reference:
|
[7] G. Streng: Linear algebra and its applications.Academic Press, New York (1976) (Russian translation, Izdat. Mir, Moskva, 1980). |
| Reference:
|
[8] V. Šeda: On the existence of oscillatory solutions in the Weisbuch-Salomon-Atlan model for the Belousov-Zhabotinskij reaction.Apl. Mat. 23 (2978), 280-294. MR 0495430 |
| Reference:
|
[9] Y. Takeuchi N. Adachi H. Tokumaru: The stability of generalized Volterra equations.J. Math. anal. Appl. 62 (2978), 453-473. MR 0477317 |
| Reference:
|
[10] J. J. Tyson: The Belousov-Zhabotinskij reaction.Lecture Notes in Biomathematics, Springer-Verlag, Berlin-Heidelberg-New York (1916). |
| . |
