Prog. Theor. Phys. Vol. 77 No. 6 (1987) pp. 1307-1318

[ Full Text PDF : FREE ACCESS (669K) ]

Oregonator Model with a Flow Term for the Belousov-Zhabotinskii Reaction Having Constant Feed. I

— Proposal of Model and Its Behavior —

Chiaki Murase, Shinji Sakanoue^* and Mitsuo Endo^*

Physics, Faculty of General Education, The Tokyo University of Agriculture and Technology, Fuchu 183
^*Chemistry, Faculty of General Education, The Tokyo University of Agriculture and Technology, Fuchu 183

(Received October 8, 1986)

Abstract:

A modified version of the Oregonator with a flow term is proposed to study experimental results on the Belousov-Zhabotinskii reaction having constant feed. Our model can properly exhibit the following three characteristic behaviors in oscillations of the concentration of Br^-; i.e., the existence of two oscillations with a large and a small amplitude, multipeak oscillations and a mixing of two types of oscillations which we call mixing phenomena. We have examined our model by simulations and shown how these characteristic behaviors occur. Especially a semi-global behavior around a stationary state is examined in connection with the mixing phenomena.

URL : http://ptp.ipap.jp/link?PTP/77/1307/
DOI : 10.1143/PTP.77.1307

References:

B. P. Belousov, Ref. Radiats. Med. 1958 (1959), 145.
A. M. Zhabotinskii, Dokl. Akad. Nauk SSSR 157 (1964), 392; ibid. Biofizika 9 (1964), 306.
R. J. Field, E. Körös and R. M. Noyes, J. Am. Chem. Soc. 94 (1972), 8649[CrossRef].
R. J. Field and R. M. Noyes, J. Chem. Phys. 60 (1974), 1877[CrossRef].
J. J. Tyson, J. Chem. Phys. 66 (1977), 905[CrossRef].
R. A. Schmitz, K. R. Graziani and J. L. Hudson, J. Chem. Phys. 67 (1977), 3040[CrossRef].
J. L. Hudson, M. Hart and D. Marinko, J. Chem. Phys. 71 (1979), 1601[CrossRef].
C. Vidal, S. Bachelart and A. Rossi, J. de Phys. 43 (1982), 7.
J. C. Roux, Physica 7D (1983), 57[Elsevier].
K. Showalter, R. M. Noyes and K. Bar-Eli, J. Chem. Phys. 69 (1978), 2514[CrossRef].
J. J. Tyson, J. Math. Biol. 5 (1978), 351.
K. Tomita and I. Tsuda, Phys. Lett.71A (1979), 489.
R. D. Janz, D. J. Vanecek and R. J. Field, J. Chem. Phys. 73 (1980), 3132[CrossRef].
K. Imaeda and T. Tei, J. Phys. Soc. Jpn. 55 (1986), 743[JPSJ].
K. Tomita and I. Tsuda, Prog. Theor. Phys. 64 (1980), 1138[PTP].
I. Tsuda, Phys. Lett. 85A (1981), 4.
I. Tsuda and K. Tomita, "Nonequilibrium Statistical Physics Problems in Fusion Plasmas -Stochasticity and Chaos-", Proc. of US-Japan Workshop, 1981, Kyoto, p. 131.
C. Lobry and R. Lozi, Nonlinear Phenomena in Chemical Dynamics (Springer Series in Synergetics 12, 1981), p. 67.
C. Murase, S. Sakanoue and M. Endo, Prog. Theor. Phys. 77 (1987),.
S. Sakanoue, C. Murase, and M. Endo, Bull. Chem. Soc. Jpn. 56 (1983), 2380[CrossRef].
C. Murase and S. Sakanoue, Prog. Theor. Phys. 69 (1983), 742[PTP].
M. J. Feigenbaum, J. Stat. Phys. 19 (1978), 25[CrossRef].
K. Kaneko, Prog. Theor. Phys. 68 (1982), 669[PTP]; ibid. 69 (1983), 403[PTP]; ibid. 69 (1983), 1427[PTP].
Y. Pomeau and P. Manneville, Comm. Math. Phys. 74 (1980), 189.

Citing Article(s) :

Progress of Theoretical Physics Vol. 77 No. 6 (1987) pp. 1319-1333 :
Oregonator Model with a Flow Term for the Belousov-Zhabotinskii Reaction Having Constant Feed. II

Chiaki Murase, Shinji Sakanoue and Mitsuo Endo