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 0167-2789/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)