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Electrically Coupled Belousov-Zhabotinskii Oscillators: Experimental Observation of Chaos in a Chemical System and Identification of its Source in the Field-Noyes Equations

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Nonlinear Oscillations in Biology and Chemistry

Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 66))

Abstract

The Belousov-Zhabotinskii (BZ) reaction is by far the chemical oscillator that is best characterized experimentally and best understood mechanistically (Field et al. 1972; Field 1985; Field and Boyd, 1985). It is the metal-ion-catalyzed oxidation by bromate ion (BrO -3 ) of any of a large class of organic materials in a strongly acidic, aqueous medium. In the experiments reported here, the Ce(IV)/Ce(III) couple is used as the metal-ion catalyst and acetylacetone (CH3COCH2-COCH3), which we will refer to as AA, is used as the organic material to avoid bubble formation. All experiments were carried out in 2.73 M H2SO4 and in continuous-flow, stirred tank reactors (CSTR) driven by peristaltic pumps. The general behavior of oscillating chemical reactions in CSTR experiments has been reviewed by DeKepper and Boissonade (1985), and the detailed CSTR behavior of the BZ reaction with malonic acid has been described by DeKepper and Bar-Eli (1983).

This work partially supported by the National Science Foundation under Grant CHE 80–23755.

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References

  1. Bar-Eli, K. and Haddad, S., 1979, The Belousov-Zhabotinskii Reaction. Comparison of Experiments and Calculations, J. Phys. Chem., 83, 2944.

    Article  Google Scholar 

  2. Bar-Eli, K., 1984a, Coupling of Chemical Oscillators, J. Phys. Chem., 88, 3616.

    Article  Google Scholar 

  3. Bar-Eli, K., 1984b, The Dynamics of Coupled Oscillators, J. Phys. Chem., 88, 6174.

    Article  Google Scholar 

  4. Bar-Eli, K. and Ronkin, J., 1984, Oscillations and Steady States in the Bromate-Bromide-Cerous System: Comparison of Experimental and Calculated Data of Different Sets of Rate Constants, J. Phys. Chem., 88, 2844.

    Article  Google Scholar 

  5. Bar-Eli, K., 1985, The Peristaltic Effect on Chemical Oscillations, J. Phys. Chem., 89, in press.

    Google Scholar 

  6. Bar-Eli, K. and Reuveni, S., 1985, Stable Stationary States of Coupled Chemical Oscillators. Experimental Evidence, J. Phys. Chem., 89, 1329.

    Article  Google Scholar 

  7. Bard, A.J. and Faulkner, J.R., 1980, Electrochemical Methods, Wiley, New York.

    Google Scholar 

  8. Becker, P.K. and Field, R.J., 1985, Stationary Concentration Patterns in the Oregonator Model of the Belousov-Zhabotinskii Reaction, J. Phys. Chem., 89, 118.

    Article  Google Scholar 

  9. Boissonade, J. and DeKepper, P., 1980, Transitions from Bistability to Limit Cycle Oscillations. Theoretical Analysis and Experimental Evidence in An Open Chemical System, J. Phys. Chem., 84, 501.

    Article  Google Scholar 

  10. Buchholtz, F. and Schneider, F., 1983, First Experimental Demonstration of Chemical Resonance in An Open System, J. Am. Chem. Soc., 105, 7450.

    Article  Google Scholar 

  11. Crowley, M.F. and Field, R.J., 1981, Electrically Coupled Belousov-Zhabotinskii Oscillators: A Potential Chaos Generator, in: Nonlinear Phenomena in Chemical Dynamics (C. Vidal and A. Pacault, Eds) Springer-Verlag, Berlin, Heidelberg, and New York.

    Google Scholar 

  12. Crowley, M.F. and Field, R.J., 1984, Asymptotic Solutions of A Reduced Oregonator Model of the Belousov-Zhabotinskii Reaction, J. Phys. Chem., 88, 762.

    Article  Google Scholar 

  13. Crowley, M.F. and Field, R.J., 1985, Electrically Coupled Belousov-Zhabotinskii Oscillators. I. Experiments and Simulations, J. Phys. Chem., 89, in press.

    Google Scholar 

  14. DeKepper, P. and Bar-Eli, K., 1983, Dynamical Properties of the Belousov-Zhabotinskii Reaction in a Flow System. Theoretical and Experimental Analysis, J. Phys. Chem., 87, 480.

    Article  Google Scholar 

  15. DeKepper, P. and Boissonade, J., 1985, From Bistability to Sustained Oscillations in Homogeneous Chemical Systems in Flow Reactor Mode, in: Oscillations and Traveling Waves in Chemical Systems (R.J. Field and M. Burger, Editors), Wiley-Interscience, New York.

    Google Scholar 

  16. Field, R.J., Körös, E., and Noyes, R.M., 1972, Oscillations In Chemical Systems. I. Thorough Analysis of Temporal Oscillation in the Ce-BrO3 - -Malonic Acid-System, J. Am. Chem. Soc., 94, 8649.

    Article  Google Scholar 

  17. Field, R.J. and Noyes, R.M., 1974, Oscillations in Chemical Systems IV. Limit Cycle Behavior in A Model of A Real Chemical Reaction, J. Chem. Phys., 60, 1877.

    Article  Google Scholar 

  18. Field, R.J., 1985, Experimental and Mechanistic Characterization of Brornate-Ion-Driven Chemical Oscillations and Traveling Waves in Closed Systems, in: Oscillations and Traveling Waves in Chemical Systems (R.J. Field and M. Burger, Editors), Wiley-Interscience, New York.

    Google Scholar 

  19. Field, R.J. and Boyd, P.M., 1985, Bromine-Hydrolysis Control in the Cerium Ion-Bromate Ion- Oxalic Acid-Acetone Belousov-Zhabotinskii Oscillator, J. Phys. Chem., 89, in press.

    Google Scholar 

  20. Fujii, H. and Sawada, Y., 1978, Phase-difference Locking of Coupled Oscillating Chemical Systems, J. Chem. Phys., 69, 3830.

    Article  Google Scholar 

  21. Ganapathisubramanian, N. and Noyes, R.M., 1981, A Discrepancy Between Experimental and Computational Evidence for Chemical Chaos, J. Chem. Phys., 76, 1770.

    Article  Google Scholar 

  22. Gear, C.W., 1971, The Automatic Integration of Ordinary Differential Equations, Comm. ACM, 14, 176.

    Article  MATH  MathSciNet  Google Scholar 

  23. Guckenheimer, J., 1979, A Brief Introduction to Dynamical Systems, in: Nonlinear Oscillations in Biology, Vol. 17 of Lectures in Applied Mathematics, American Mathematical Society, Providence, Rhode Island.

    Google Scholar 

  24. Guckenheimer, J., 1981, On Codimension Two Bifurcation, Dynamical Systems and Turbulence, Warwick, 1980, Lecture Notes in Mathematics, Vol. 898, (D.R. and L.S. Young, Editors) Springer-Verlag, Berlin.

    Google Scholar 

  25. Heilweil, E.J. and Epstein, I.R., 1979, Chemical Oscillations and Chaos in A Single System, J. Phys. Chem., 83, 1359.

    Article  Google Scholar 

  26. Holmes, P., 1980a, Averaging and Chaotic Motions in Forced Oscillations, SIAM J. Appl. Math., 38, 65.

    Article  MATH  MathSciNet  Google Scholar 

  27. Holmes, P., 1980b, Phase Locking and Chaos in Coupled Limit Cycle Oscillations, Proc. Symp. on Recent Advances on Structural Dynamics, Southampton, Great Britain.

    Google Scholar 

  28. Janz, R.D., Vanecek, D.J., and Field, R.J., 1980, Composite Double Oscillation in a Modified Version of the Oregonator Model of the Belousov-Zhabotinskii Oscillator, J. Chem. Phys., 73, 3132.

    Article  MathSciNet  Google Scholar 

  29. Jenkins, M. and Watts, D.G., 1969, Spectral Analysis and its Applications, Holden-Day, San Francisco.

    Google Scholar 

  30. Levi, M., 1981, Qualitative Analysis of Forced Relaxation Oscillators, Mem. Am. Math. Soc., No. 244.

    Google Scholar 

  31. Marek, M. and Stuchl, I., 1975, Synchronization in Two Interacting Oscillatory Systems, Biophys. Chem., 3, 241.

    Article  Google Scholar 

  32. McKinnon, C.K. and Field, R.J., 1985, CSTR Bistability in the Belousov-Zhabotinskii Reaction: Oregonator and Explodator Models, J. Phys. Chem., 89. in press.

    Google Scholar 

  33. Minorsky, N., 1972, Nonlinear Oscillations, Van Nostrand, New York; reprinted by Krieger, Huntington, New York (1974).

    Google Scholar 

  34. Nakajima, K. and Sawada, Y., 1980, Experimental Studies on the Weak Coupling of Oscillatory Chemical Reaction Systems, J. Chem. Phys., 72, 2231.

    Article  Google Scholar 

  35. Noszticzius, Z., 1979, Non-Br--Controlled Oscillations in the Belousov-Zhabotinskii Reaction of Malonic Acid, J. Am. Chem. Soc., 101, 3177.

    Article  Google Scholar 

  36. Noszticzius, Z. and Bodiss, J., 1975, A Heterogeneous Chemical Oscillator, The Belousov-Zhabotinskii Type Reaction of Oxalic Acid, J. Am. Chem. Soc., 101, 3660.

    Article  Google Scholar 

  37. Noszticzius, Z., Noszticzius, E., and Schelly, Z.A., 1984, Explodator: A New Skeleton Mechanism for Halate Driven Chemical Oscillators, J. Chem. Phys., 80, 6062.

    Article  MathSciNet  Google Scholar 

  38. Noszticzius, Z., Gáspár, V., and Försterling, H.-D., 1985, Experimental Test for the Control Intermediate in the Belousov-Zhabotinskii (BZ) Reaction, J. Am. Chem. Soc., 107, 2314.

    Article  Google Scholar 

  39. Noyes, R.M., 1985, An Alternative to the Stoichiometric Factor in the Oregonator Model, J. Chem. Phys., 80, 6071.

    Article  MathSciNet  Google Scholar 

  40. Rehmus, P. and Ross, J., 1985, Periodically Perturbed Chemical Systems, in: Oscillations and Traveling Waves in Chemical Systems (R.J. Field and M. Burger, Editors) Wiley-Interscience, New York.

    Google Scholar 

  41. Rinzel, J. and Troy, W.C., 1982, Bursting Phenomena in a Simplified Oregonator Flow System Model, J. Chem. Phys., 76, 1775.

    Article  MathSciNet  Google Scholar 

  42. Rössler, O.E., 1979, Chaos, in: Structural Stability in Physics (W. Güttinger and H. Eikemeir, Editors) Springer-Verlag, Berlin, Heildelberg, New York.

    Google Scholar 

  43. Roux, J.-C, 1983, Experimental Studies of Bifurcations Leading to Chaos in the Belousov-Zhabotinskii Reaction, Physica D, 7D, 57.

    Article  MathSciNet  Google Scholar 

  44. Roux, J.-C, Simoyi, R.H., and Swinney, H.L., 1983, Observation of A Strange Attractor, Physica D, 8D, 257.

    Article  MathSciNet  Google Scholar 

  45. Ruoff, P. and Schwitters, R., 1984, Theoretical Study of Ag+ -Induced Oscillations and Excitations in the Classical Homogeneous Belousov-Zhabotinsky Reaction Using the Oregonator Model, J. Phys. Chem., 88, 6424.

    Article  Google Scholar 

  46. Schreiber, I. and Marek, M, 1982, Strange Attractors in Coupled Reaction Diffusion Cells, Physica D, 5D, 258.

    Article  MathSciNet  Google Scholar 

  47. Smale, S., 1965, Diffomorphisms with Many Periodic Points, in: Differential and Combinatorial Topology (S.S. Cairns, Editor) Princeton University Press, Princeton, N.J.

    Google Scholar 

  48. Smale, S., 1967, Differentiable Dynamical Systems, Bull. Am. Math. Soc., 73, 747.

    Article  MATH  MathSciNet  Google Scholar 

  49. Swinney, H.L., 1983, Observations of Order and Chaos in Nonlinear Systems, Physica D, 7D, 3.

    Article  MathSciNet  Google Scholar 

  50. Stuchl, I. and Marek, M., 1982, Dissipative Structures in Coupled Cells: Experiments, J. Chem. Phys., 77, 2956.

    Article  Google Scholar 

  51. Troy, W.C., 1985, A Quantitative Account of Oscillations, Bistability and Traveling Waves in the Belousov-Zhabotinskii Reaction, in; Oscillations and Traveling Waves in Chemical Systems (R.J. Field and M. Burger, Editors), Wiley-Interscience, New York.

    Google Scholar 

  52. Tyson, J.J. and Fife, P., 1980, Target Patterns in a Realistic Model of the Belousov-Zhabotinskii Reaction, J. Chem. Phys., 73, 2224.

    Article  MathSciNet  Google Scholar 

  53. Tyson, J.J., 1982, Scaling and Reducing the Field-Körös-Noyes Mechanism of the Belousov-Zhabotinskii Reaction, J. Phys. Chem., 86, 3006.

    Article  Google Scholar 

  54. Tyson, J.J., 1985, Mathematical Analysis of the Oregonator Model of the Belousov-Zhabotinskii Reaction, in: Oscillations and Traveling Waves in Chemical Systems (R.J. Field and M. Burger, Editors), Wilev-Interscience. New York.

    Google Scholar 

  55. Varga, M., Györgyi, L., and Koros, E., 1985, A Thorough Study of Bromide Control in Bromate Oscillators. 2. Simulation by the Oregonator Model of the Behavior of the Reacting Belousov-Zhabotinskii Systems Perturbed by Bromo-Complex-Forming Metal Ions, J. Phys. Chem., 89, 1019.

    Article  Google Scholar 

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Crowley, M.F., Field, R.J. (1986). Electrically Coupled Belousov-Zhabotinskii Oscillators: Experimental Observation of Chaos in a Chemical System and Identification of its Source in the Field-Noyes Equations. In: Othmer, H.G. (eds) Nonlinear Oscillations in Biology and Chemistry. Lecture Notes in Biomathematics, vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93318-9_5

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  • DOI: https://doi.org/10.1007/978-3-642-93318-9_5

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