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Field-Körös-Noyes’ model; Belousov-Zhabotinskij reaction; Lyapunov function; equilibrium point; stability in the large
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.
[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
[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. DOI 10.1063/1.1681288
[3] P. Hartman: Ordinary Differential Equations. J. Wiley and Sons, New York-London-Sydney (1964) (Russian translation, Izdat Mir, Moskva, 1970). MR 0171038 | Zbl 0125.32102
[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
[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).
[6] J. D. Murray: On a model for temporal oscillations in the Belousov-Zhabotinskij reaction. J. Chem. Phys. 6 (1975), 3610-3613.
[7] G. Streng: Linear algebra and its applications. Academic Press, New York (1976) (Russian translation, Izdat. Mir, Moskva, 1980).
[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
[9] Y. Takeuchi N. Adachi H. Tokumaru: The stability of generalized Volterra equations. J. Math. anal. Appl. 62 (2978), 453-473. MR 0477317
[10] J. J. Tyson: The Belousov-Zhabotinskij reaction. Lecture Notes in Biomathematics, Springer-Verlag, Berlin-Heidelberg-New York (1916).
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