Physica 29D (1988) 409-415
North-Holland, Amsterdam
NONSTATIONARY ROTATION OF SPIRAL WAVES: THREE-DIMENSIONAL EFFECT
K.I. AGLADZE, A.V. PANFILOV and A.N. RUDENKO
Institute of Biological Physics, Pushchino, Moscow 142292, USSR
Received 7 May 1986
Revised manuscript received 10 July 1987
Nonstationary rotation of spiral waves was studied in experiments with the chemical active medium (the
Belousov-Zhabotinsky reaction). It was shown that nonstationarity in some cases is a result of nonuniformity of the reaction
throughout the solution depth due to nonuniform saturation with oxygen from the surface to bottom of the solution.
Numerical experiments confirm the experimental data. It was shown numerically that this type of nonuniformity can lead to
nonstationary rotation of spiral waves.
1. Introduction
The origination of spiral waves rotation is a
universal property of active media of various na-
tures. These waves have been observed in
a wide range of active media: cardiac muscle [1],
the morphogenesis processes of social amoeba
D. Discoiseum [2], the Belousov-Zhabotinsky (BZ)
reaction [3], nerve tissue [4], etc. The BZ chemical
active medium, representing a thin layer of a
solution in which the BZ reaction proceeds [3, 5,
6] is the most suitable system for the investigation
of spiral waves. It has been used for studying the
origination, death and reproduction of spiral waves
[7].
Of particular interest is a chaotic behaviour of
the sources in an active medium. It has been
shown for the chemical active medium that the
induced inhomogeneity results in a chaotic repro-
duction of spiral waves making the propagation of
excitations in the active medium impossible [7].
An analogous scheme was suggested to explain the
heart fibrillation [8].
More subtle effects may be due to the occur-
rence of a strange attractor [9] in the system of
equations describing the reaction. In particular, it
was suggested that it may cause a nonstationary
meandering of the tip of a spiral wave during
rotation [6]. It was also noted that nonstationary
rotation of waves is always observed in a chemical
active medium [6, 11]. This fact seems to be essen-
tial since all the mathematical models of spiral
waves have been constructed with the assumption
of stationary rotation [12] and the computational
experiments exhibit both stationary [13] and non-
stationary rotations [14].
Therefore we undertook a detailed study of the
spiral wave rotation in a chemical active medium.
2. Experimental studies in the chemical
active medium
2.1. Methods
Experimental studies of autowave processes in
chemical systems utilized a thin layer of BZ reac-
tion mixture spread over the bottom of a Petri
dish [5, 6]. The composition of the medium was
close to that proposed by Winfree [6]: 0.3M
NaBrO3; 0.1M CHBr (COOH)2; 0.15-0.45M
H2SO4, 1-SmM ferroin. A Petri dish, 9 cm in
diameter, was filled with 4 ml of the reagent and
placed on a transparent thermostated platform
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