Stability of a model for the Belousov-Zhabotinskij reaction
Haluška, Vladimír
Applications of Mathematics, Tome 34 (1989), p. 89-104 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1989-01-01
Classification:  34D20,  80A30 
@article{104338,
     author = {Vladim\'\i r Halu\v ska},
     title = {Stability of a model for the Belousov-Zhabotinskij reaction},
     journal = {Applications of Mathematics},
     volume = {34},
     year = {1989},
     pages = {89-104},
     zbl = {0681.34047},
     mrnumber = {0990297},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104338}
}

Haluška, Vladimír. Stability of a model for the Belousov-Zhabotinskij reaction. Applications of Mathematics, Tome 34 (1989) pp. 89-104. http://gdmltest.u-ga.fr/item/104338/

K. Bachratý On the stability of a model for the Belousov-Zhabotinskij reaction, Acta mathematica Univ. Comen. XLII-XLIII (2983), 225-234. | MR 0740754

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. (1974) | Article

P. Hartman Ordinary Differential Equations, J. Wiley and Sons, New York-London-Sydney (1964) (Russian translation, Izdat Mir, Moskva, 1970). (1964) | MR 0171038 | Zbl 0125.32102

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. (1976) | MR 0457858

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). (1964)

J. D. Murray On a model for temporal oscillations in the Belousov-Zhabotinskij reaction, J. Chem. Phys. 6 (1975), 3610-3613. (1975)

G. Streng Linear algebra and its applications, Academic Press, New York (1976) (Russian translation, Izdat. Mir, Moskva, 1980). (1976)

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

Y. Takeuchi N. Adachi H. Tokumaru The stability of generalized Volterra equations, J. Math. anal. Appl. 62 (2978), 453-473. | MR 0477317

J. J. Tyson The Belousov-Zhabotinskij reaction, Lecture Notes in Biomathematics, Springer-Verlag, Berlin-Heidelberg-New York (1916). (1916)