2848
J . Phys. Chem. 1984,88, 2848-2851
Experimental Study of Complex Dynamical Behavior in Coupled Chemical Oscillators‘ Mohamed Alamgir and Irving R. Epstein* Department of Chemistry, Brandeis University, Waltham, Massachusetts 02254 (Received: September 29, 1983)
The dynamical behavior of two systems of coupled chemical oscillators, Br03--C102--I- (Br03--r plus CIOz--I-) and Br03--I--Mn2+ (Br03--I- plus Br03--Br--Mn2+) has been studied. In the former system, where the coupling is strong, several new features not present in the uncoupled subsystems such as birhythmicity, compound oscillation, and complex periodic and aperiodic oscillation emerge. The behavior of this system is mapped as the flow rate, temperature, input concentrations, and acidity are varied. The latter system, in which the coupling is weaker, shows phenomena more easily identified with the uncoupled oscillators plus a region of tristability.
Introduction Since the acceptance of oscillatory chemical reactions as fact rather than artifact, the thrust of experimental work on these systems has been toward three major goals: mechanistic understanding of known chemical oscillators, the development of new oscillating reactions, and the discovery of other dynamical phenomena associated with chemical oscillation. Among the phenomena related to periodic oscillation are multiple steady states (bistability, tristability, birhythmicity), complex oscillations, and chemical chaos. Not surprisingly, it has been the BelousovZhabotinskii (BZ) reaction, the most extensively studied chemical oscillator, which has proved to be the most abundant source thus far of new dynamical phenomena. However, with the successful development of a variety of new chemical oscillators, particularly those involving ~ h l o r i t e the , ~ possibility of generating complex dynamical behavior by chemically coupling two or more different oscillators becomes an attractive one. Most earlier studies of coupled chemical oscillators have utilized the BZ or related systems and have been of two types. Chemically identical systems have been coupled physically, e.g., by mass flow between two tank reactors, and chemically different systems have been linked chemically in a single vessel through common reactants or intermediates. Some physical coupling experiments4v5have been devoted primarily to the study of relative stabilities of steady states rather than to the possible varieties of oscillations under such conditions. Others have studied BZ systems under oscillatory conditions and linked either electrochemically6 or by mass t r a n ~ p o r t . The ~ earliest chemical coupling experiments, carried out in closed (batch) systems involved the use of two or more organic substrates in a single BZs or Briggs-Rauscher os~illator.~ Similar phenomena were observed in both cases-a burst of oscillations characteristic of one substrate followed by a quiescent period and then by a second set of oscillations associated with the other substrate. The first such experiments in an open (CSTR) system were performed by Maselko,lowho investigated the behavior of BZ-type systems containing mixed malonic acid-citric acid and malonic (1) Part 19 in the series Systematic Design of Chemical Oscillators. Part 18: Ahlstrom, C.; Boyd, D.; Epstein, I. R.; Kustin, K.; Romanow, J. Inorg. Chem., in press. (2) For a review, see: Epstein, I. R.; Kustin, K.; De Kepper, P.; Orbfin, M. Sci. Am. 1983, 248, 112-23. (3) Orbtin, M.; Dateo, C.; De Kepper, P.; Epstein, I. R. J. Am. Chem. SOC. 1982,104, 5911-18. (4) Bar-Eli, K.; Geiseler, W. J . Phys. Chem. 1981, 85, 3461-8. (5) Stuchl, I.; Marek, J. J . Chem. Phys. 1982, 77, 2956-63. (6) Crowley, M. F.; Field, R. J. In “Nonlinear Phenomena in Chemical Dyanamics”; Vidal, C., Pacault, A., Eds.; springer-Verlag: West Berlin, 1981; pp 147-53. (7) Marek, M.; Stuchl, I. Biophys. Chem. 1975, 3, 241-8. (8) Heilweil, E. J.; Henchman, M. J.; Epstein, I. R. J . Am. Chem. SOC. 1979, 101, 3698-700. (9) Cooke, D. 0. Int. J . Chem. Kinet. 1982, 14, 1047-51. (10) Maselko, J. Chem. Phys. 1983, 78, 381-9.
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acid-oxaloacetic acid substrates. Phase diagrams were determined and showed several regions of complex oscillation characteristic only of the mixed and not of the uncoupled systems. Particular attention was devoted to the bifurcation behavior of the system. Recently, Decroly and Goldbeter” analyzed a model consisting of two allosteric enzymes coupled so that the product of one enzyme constitutes the substrate of the other. This coupling of two nonlinear oscillators generates a wide range of dynamical phenomena including birhythmicity-the coexistence of two different stable oscillatory modes for the same set of external parameters-and chaos. In an earlier communication12we reported preliminary results obtained by coupling the two independently oscillatory systems: chlorite-iodide and bromate-iodide. In the C102--Br0
