Types of oscillations in chemical reactions

  • Okan Gurel
  • Demet Gurel
Conference paper
Part of the Topics in Current Chemistry book series (TOPCURRCHEM, volume 118)


Malonic Acid Continuous Stir Tank Reactor Stable Limit Cycle Oscillatory Solution Limit Cycle Oscillation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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VIII References

  1. (IIID).
    1958 Aris, R., Amundson, N. R.: An Analysis of Chemical Reactor Stability and Control. II. The Evolution of Proportional Control, Chem. Eng. Sci. vol. 7, 132–147CrossRefGoogle Scholar
  2. (IIIA).
    1911 Auger, V.: Action de l'eauxoxygenee sur les composes oxygenes de l'iode, Compt. rendus. vol. 153, 1005–1007Google Scholar
  3. (IIIC).
    1959 Belousov, B. P.: Sb. Ref. Radiats. Med. 1958, Medzig (Moscow) p. 145. (1958 Collection of Abstracts on Radiation Medicine)Google Scholar
  4. (IIIE).
    1973 Belyaev, V. D., Slin'ko, M. M., Timoshenko, V. I., Slin'ko, M. G.: Generation of Auto-Oscillations in the Hydrogen Reaction on Nickel, Kinetics and Catalysis, vol. 14, 708–709Google Scholar
  5. (IIIE).
    1972 Beusch, H., Fieguth, P., Wicke, E.: Thermisch und kinetisch verursachte Instabilitäten im Reaktionsverhalten einzelner Katalysatorkorner, Chem. Ing. Tech. vol. 44, 445–451 See also (1972) Unstable Behavior of Chemical Reactions at Single Catalyst Particles, In: Chemical Reaction Engineering Reviews, Advances in Chemistry Series (ed. Gould, R. F.) 109, American Chemical Society, Washington, D.C. 615–621.CrossRefGoogle Scholar
  6. (IIID).
    1955 Bilous, O., Amundson, N. R.: Chemical Reactor Stability and Sensitivity, A. I. CH. E. Journal vol. 1, 513–521Google Scholar
  7. (IIIB).
    1976 Boissonade, J.: Aspect theoriques de la “double oscillation” dans les systemes dissipatifs chimiques J. Chimie de Physique, vol. 73, 540–544Google Scholar
  8. (IIIB).
    1980 Boissonade, J., De Kepper, P.: Transitions from Bistability to Limit Cycle Oscillations. Theoretical Analysis and Experimental Evidence in an Open Chemical System. J. Phys. Chem. vol. 84, 501–506Google Scholar
  9. (IIIA).
    1921 Bray, W. C.: A Periodic Reaction in Homogeneous Solution and its Relation to Catalysis. J. Amer. Chem. Soc. vol. 43, 1262–1267CrossRefGoogle Scholar
  10. (IIIA).
    1931 Bray, W. C., Caulkins, A. L.: Reactions Involving Hydrogen Peroxide, Iodine and Iodate Ion: II. The Preparation of Iodic Acid. Preliminary Rate Measurements. J. Amer. Chem. Soc. vol. 53, 44–48CrossRefGoogle Scholar
  11. (IIIA).
    1931 Bray, W. C., Liebhafsky, H. A.: Reactions Involving Hydrogen Peroxide, Iodine and Iodate Ion. I. Introduction, J. Amer. Chem. Soc. vol. 53, 38–44CrossRefGoogle Scholar
  12. (IIIC).
    1935 Bray, W. C., Liebhafsky, H. A.: The Kinetic Salt Effect in the Fourth Order Reaction BrO3+Br+2H+ →. Ionization Quotients for HSO4 at 25°, SO4 at 25°. J. Amer. Chem. Soc. vol. 57, 51–56CrossRefGoogle Scholar
  13. (IIIB).
    1973 Briggs, T. S., Rauscher, W. C.: An Oscillating Iodine Clock, J. Chemical Education, vol. 50, 496Google Scholar
  14. (IIIC).
    1980 Burger, M., Koros, E.: Conditions for the Onset of Oscillations, J. Phys. Chem. vol. 84, 496–500Google Scholar
  15. (IIIF).
    1964 Chance, B., Hess, B., Betz, A.: DPNH Oscillations in a Cell-free Extract of S. Carlsbergensis, Biochem. and Biophys. Res. Commun. vol. 16, 182–187Google Scholar
  16. (IIIA).
    1967 Degn, H.: Evidence of a Branched Chain Reaction in the Oscillating Reaction of Hydrogen Peroxide, Iodine and Iodate, Acta Chem. Scand. vol. 21, 1057–1066Google Scholar
  17. (IIIC).
    1967 Degn, H.: Effect of Bromine Derivatives of Malonic Acid on the Oscillating Reaction of Malonic Acid, Cerium Ions and Bromate, Nature, vol. 213, 589–590Google Scholar
  18. (IIIG).
    1968 Degn, H.: Bistability Caused by Substrate Inhibition of Peroxidase in an Open Reaction System, Nature vol. 217, 1047–1050PubMedGoogle Scholar
  19. (IIIG).
    1969 Degn, H.: Compound III Kinetics and Chemiluminescence in Oscillatory Oxidation Reaction Catalyzed by Horseradish Peroxidase, Biochem. Biophysica Acta, vol. 180, 271–290Google Scholar
  20. (IIIG).
    1969 Degn, H., Mayer, D.: Theory of Oscillations in Peroxidase Catalyzed Oxidation Reactions in Open System, Biochimica et Biophysica Acta, vol. 180, 291–301PubMedGoogle Scholar
  21. (R1).
    1972 Degn, H.: Oscillating Chemical Reactions in Homogeneous Phase, J. Chem. Education, vol. 49, no. 5, 302–307Google Scholar
  22. (IIIB).
    1976 De Kepper, A. A. Pacault, Rossi, A.: d'une reaction chimique periodique, multistationnaire et transitions, C. R. Acad. Sci. Paris, Ser. C, vol. 282, 199–204Google Scholar
  23. (IIIH).
    1974 DePoy, P. E., Mason, D. M.: Periodicity in Chemically Reacting Systems. In: Faraday Symposia of the Chemical Society, No. 9, Physical Chemistry of Oscillatory Penomena, 47–54Google Scholar
  24. (IIIF).
    1957 Duysens, L. N., Amesz, M. J.: Fluorecence Spectrophotometry of Reduced Phosphorpyridine Nucleotide in Intact Cells in the Near-ultraviolet and Violet Region., Biochem. Biophys. Acta, vol. 24, 19–26PubMedGoogle Scholar
  25. (IIIF).
    1973 Dynnik, V. V., Sel'kov, E. E., Semashko, L. R.: Analysis of the Adennine Nucleotide Effect on the Oscillatory Mechanism in Glycolysis, Studia Biophysica, vol. 41, 193–214Google Scholar
  26. (IIIF).
    1975–1 Dynnik, V. V., Sel'kov, E. E.: Generator of Oscillations in the Lower Part of the Glycolytic System, Biophysics vol. 20, 292–297 (Biofizika, 288–292)Google Scholar
  27. (IIIF).
    1975–2 Dynnik, V. V., Sel'kov, E. E.: Double-Frequency Oscillations in the Glycolytic System. Mathematical Model, Biophysics vol. 20, 297–309 (Biofzika, 293–397).Google Scholar
  28. (IIIE).
    1973 Eckert, E., Hlavacek, V., Marek, M.: Catalytic Oxidation of CO On CuO · Al2O3, I. Reaction Rate Model Discrimination, Chem. Eng. Comm. vol. 1, 89–94. II. Measurement and Description of Hysteresis and Oscillations in a Laboratory Catalytic Recycle Reactors Chem. Eng. Com. vol. 1, 95–102Google Scholar
  29. (IIIE).
    1973 Eckert, E., Hlavacek, V., Kubicek, M., Sinkule, J., Zur Kenntnis des Zweiphasen-modells des Katalytischen Reaktors, Chem. Ing. Tech. vol. 45, 83–88CrossRefGoogle Scholar
  30. (IIIA).
    1979 Edelson, D., Noyes, R. M.: Detailed Calculations Modeling the Oscillatory Bray-Liebhafsky Reaction, J. Phys. Chem. vol. 83, 212–220Google Scholar
  31. (IIIE).
    1976 Eigenberger, G.: Kinetic Instabilities in Catalytic Reactions-A Modeling Approach, 4th Int. Symp. on Chem. Reaction Engineering, Heidelberg, 290–299Google Scholar
  32. (IIIC).
    1972 Field, R. J., Koros, E., Noyes, R. M.: Oscillations in Chemical Systems II. Thorough Analysis of Temperal Oscillations in the Bromate-Cerium-Malonic Acid System., J. Amer. Chem. Soc. vol. 94, 8649–8664CrossRefGoogle Scholar
  33. (IIIC).
    1974 Field, R. J., Noyes, R. M.: Oscillations in Chemical Systems, IV. Limit Cycle Behavior in a Model of Chemical Reaction, J. Chem. Phys. vol. 60, 1877–1884Google Scholar
  34. (R12).
    1978 Franck, U. F.: Chemical Oscillations, Angew. Chem. vol. 90, 1–16. (International Edition in English vol. 17, 1–15)Google Scholar
  35. (R8).
    1976 Goldbeter, A., Caplan, S. R.: Oscillatory Enzymes, Ann. Rev. of Biophys. and Bioeng. vol. 5, 449–476CrossRefGoogle Scholar
  36. (IIIF).
    1964 Gosh, A., Chance, B.: Oscillations of Glycolytic Intermediates in Yeast Cells, Biochem. Biophys. Res. Commun. vol. 16, 174–181PubMedGoogle Scholar
  37. (R5).
    1974 Gray, B. F., Aarons, L. J.: Small Parasitic Parameters and Chemical Oscillations, In: Physical Chemistry of Oscillatory Phenomena, Symposium of the Faraday Society, No. 9, Faraday Division, Chemical Society, London, 129–136Google Scholar
  38. (R15).
    1980 Gray, B. F.: Thermokinetic Oscillations in Gaseous System Kinetics of Physico-chemicals Oscillations, Berichte der Bunsen-Gesellschaft für Physikalische Chemie, vol. 84, no. 4, 309–315Google Scholar
  39. (IIIG).
    1975 Gurel, Demet: Dynamics of Thyroglobulin Iodination, 5th Int. Biophysics Congress, Copenhagen, Abstract P-438, p. 124Google Scholar
  40. (IIIG).
    1976 Gurel, Demet, Gans, P. J.: Kinetics of Enzymatic Thyroid Iodination, NIH NIAMD IF32 AM05373 (Unpublished work)Google Scholar
  41. (IIIG).
    1977 Gurel, Demet, McNelis, E.: Oscillating Reactions in the Iodination of Thyroglobulin, NIH NIAMD 1R01 AM20850 (Unpublished work)Google Scholar
  42. (IIID).
    1965 Gurel, O., Lapidus, L.: Liapunov Stability Analysis of Systems with Limit Cycles, Chem. Eng. Symposium Seties, vol. 61, no. 55, 78–87Google Scholar
  43. (R2).
    1972 Gurel, O.: Bifurcation Theory in Biochemical Dynamics, In: Analysis and Simulation of Biochemical Systems, (Hemker, H. C., Hess, B. eds.) FEBS vol. 25, North-Holland, Amsterdam, 81–85Google Scholar
  44. (IIIJ).
    1973 Gurel, O.: Topological Dynamics in Neurobiology, Int. J. Neuroscience, vol. 6, 165–179Google Scholar
  45. (R6).
    1975 Gurel, O.: Limit Cycles and Bifurcations in Biochemical Dynamics Biosystems., vol. 7, 83–91Google Scholar
  46. (IIIJ).
    1977 Gurel, O.: Decomposed Partial Peeling and Limit Bundles Physics Letter, vol. 61A, 219–223Google Scholar
  47. (R16).
    1979–1 Gurel, O.: Some New Types of Oscillations, Kinetics of Physico-chemical Oscillations Discussion Meeting held by Deutsche Bunsengesellschaft für Physikalische Chemie, Aachen, vol. II, 486–494Google Scholar
  48. (VB).
    1979–2 Gurel, O.: Poincare Bifurcation Analysis, In: Gurel and Rossle (Book B4) p. 5–22Google Scholar
  49. (IIIJ).
    1979 Gurel, O., Rossler, O. E.: Bifurcation to Toroidal Surfaces, Math. Japonica, vol. 23, 491–507Google Scholar
  50. (IIIJ).
    1981 Gurel, O.: Exploded Points, Z. Naturforschung, vol. 36A, 72–75Google Scholar
  51. (IIIF).
    1964 Higgins, J.: A Chemical Mechanism for Oscillations of Glycolytic Intermediates in Yeast Cells, Proc. N.A.S. (USA) vol. 51, 989–994Google Scholar
  52. (IIIF).
    1967 Higgins, J.: The Theory of Oscillating Reactions, J. Ind. Eng. Chem. vol. 59, no. 5, 18–62CrossRefGoogle Scholar
  53. (R11).
    1978 Hlavacek, V., Votruba, J.: Hysteresis and Periodic Activity Behavior in Catalytic Chemical Reaction Systems, Advances in Catalysis vol. 27, 59–96Google Scholar
  54. (IIIE).
    1972 Horak, J., Jiracek, F.: Dynamic Behavior of Catalytic Flow Reactors, Chem. React. Eng., Proc. 5th Europ. Symp, B8, 1–12Google Scholar
  55. (IIIE).
    1968 Hugo, P.: Dynamic Behavior of Strongly Exothermic Catalytic Reactions in Open Gas Circulations (In German), Chem. React. Eng., Proc. 4th Eur. Symp. Pergamon Press, Oxford, England, (1971) 459–472Google Scholar
  56. (IIIE).
    1970 Hugo, P.: Stabilität und Zeitverhalten von Durfenss-Kreislauf-Reaktoren, Ber. Binsengesellschaft, Phys. Chem. vol. 74, 121–127Google Scholar
  57. (IIIE).
    1972 Hugo, P., Jakubith, M.: Dynamisches Verhalten und Kinetik der Kohlenmonoxid-Oxidation am Platin-Katalysator, Chem.-Ing.-Tech. vol. 44, 383–387CrossRefGoogle Scholar
  58. (IIIF).
    1975 Kaimachnikov, N. P., Sel'kov, E. E.: Hysteresis and Multiplicity of Dynamics States in an Open Two-Substrate Enzymatic Reaction with Substrate Depression, Biophysics, vol. 20, no. 4, 713–718 (Biofizika, 703–708)Google Scholar
  59. (IIIE).
    1979 Kaimachnikov, N. P., Schulmeister, T.: Evolution of the Limit Cycle in a Model of an Enzymatic Reaction with Substrate Deposition, Studia Biophysica, vol. 75, Heft 1, 41–50Google Scholar
  60. (IIIK).
    1978 Koros, E., Orban, M.: Uncatalyzed Oscillatory Chemical Reactions, Nature, vol. 273, 371–372Google Scholar
  61. (IIIK).
    1980 Koros, E., Orban, M., Habon, I.: Chemical Oscillations during the Uncatalyzed Reaction of Aromatic Compounds with Bromate, 3. Effect of One-Electron Redox Couples on Uncatalyzed Bromate Oscillators, J. Phys. Chem., vol. 84, 559–560Google Scholar
  62. (IIII).
    1968 Lefever, R.: Stabilite de Structure dissipative, Acad. Royal des Science de Belgique, Class des Sciences, Bulletin, vol. 54, 712–719Google Scholar
  63. (IIII).
    1971 Lefever, R., Nicolis, G.: Chemical Instabilities and Substained Oscillations. J. theor. biol. vol. 30, 267–284PubMedGoogle Scholar
  64. (IIIA).
    1931-1 Liebhafsky, H. A.: Reactions involving Hydrogen Peroxide, Iodine, and Iodate. III. The Reduction of Iodate ion by Hydrogen Peroxide, J. Amer. Chem. Soc. vol. 53, 896–911CrossRefGoogle Scholar
  65. (IIIA).
    1931-2 Liebhafsky, H. A.: IV. The Oxidation of Iodine to Iodate by Hydrogen Peroxide, J. Amer. Chem. Soc. vol. 53, 2074–2090CrossRefGoogle Scholar
  66. (IIIA).
    1967 Lindblad, P., Degn, H.: A Compiler for Digital Computation in Chemical Kinetics and its Application to Oscillatory Reaction Schemes, Acta Chem. Scand. vol. 21, 791–800Google Scholar
  67. (IIIH).
    1910-1 Lotka, A.: Contribution to the Theory of Periodic Reactions, J. Phys. Chem. vol. 14, 271–274CrossRefGoogle Scholar
  68. (IIIH).
    1910-1 Lotka, A.: Contribution to the Theory of Periodic Reactions, J. Phys. Chem. vol. 14Google Scholar
  69. (IIIC).
    1975 Marek, M., Svobodova, E.: Nonlinear Phenomena in Oscillatory Systems of Homogeneous Reactions-Experimental Observations, Biophysical Chemistry, vol. 3, 263–273Google Scholar
  70. (IIIA).
    1974 Matsuzaki, I., Nakajima, T., Liebhafsky, H. A.: The Mechanism of the Oscillatory Decomposition of Hydrogen Peroxide by the I2-IO3-couple, Chem. Letters (Japan) 1463–1466Google Scholar
  71. (IIIG).
    1969 Nakamura, S., Yokota, K., Yamazaki, I.: Sustained Oscillations in a Lactoperoxidase, NADPH and O2 system Nature vol. 222, 794Google Scholar
  72. (R3).
    1973 Nicolis, G., Portnow, J.: Chemical Oscillations, Chem. Reviews, vol. 73, no. 4, 365–384CrossRefGoogle Scholar
  73. (IIIC).
    1972 Noyes, R. M., Field, R. J., Koros, E.: Oscillations in Chemical Systems, I. Detailed Mechanism in a System Showing Temporal Oscillations, J. Amer. Chem. Soc., vol. 94, 1394–1395CrossRefGoogle Scholar
  74. (R4).
    1974 Noyes, R. M., Field, R. J.: Oscillatory Chemical Reactions, Ann. Rev. Phys. Chem. vol. 25, 95–119CrossRefGoogle Scholar
  75. (R9).
    1977 Noyes, R. M.; Field, R. J.: Mechanism of Chemical Oscillations: Experimental Examples, Acc. Chem. Res. vol. 10, 273–280CrossRefGoogle Scholar
  76. (IIIG).
    1977 Olsen, L. F., Degn, H.: Chaos in an Enzyme Reaction, Nature, vol. 267, 177–178Google Scholar
  77. (IIIK).
    1979 Orban, M., Koros, E.: Chemical Oscillations during the Uncatalyzed Reaction of Aromatic Compounds with Bromate, 1. Search for Chemical Oscillators, J. Phys. Chem. vol. 82, 1672–1674CrossRefGoogle Scholar
  78. (IIIB).
    1975 Pacault, A., deKepper, P., Hanusse, P.: Description d'un Systeme Chimique dissipatif. Illustration d'un temps thermodynamique, C. R. Acad. Sci. Paris Vol. 280B, 157–161Google Scholar
  79. (IIIB).
    1975 Pacault, A., deKepper, P., Hanusse, P., Rossi, A.: Etude d'une reaction chimique periodic Diagramme des Etas, C. R. Acad. Sci. Paris vol. 281C, 215–220Google Scholar
  80. (IIIE).
    1977 Pikios, C. A., Luss, D.: Isothermal Concentration Oscillations on Catalytic Surfaces, Chem. Eng. Sci. vol. 32, 191–194CrossRefGoogle Scholar
  81. (VB).
    1885 Poincare, H.: Sur l'equilibre d'une mass fluide animee d'un movement de rotation, Acta Mathematica, vol. 7, 259–380. (See also, Oeuvres, 1952, Gauthier-Villars, Paris, vol. 7, 40–140)Google Scholar
  82. (IIIF).
    1966 Pye, K., Chance, B.: Substained Sinusoidal Oscillation of Reduced Pyridine Nucleotide in a Cell-Free Extract of Saccharomyces Carlsbergensis, Proc. N.A.S. (USA), vol. 55, 888–894Google Scholar
  83. (R14).
    1977 Ray, H. W.: Bifurcation Phenomena in Critically Reacting Systems, In: Applications of Bifurcation Theory (P. H. Rabinowitz, ed.) Academic Press, 285–315Google Scholar
  84. (IIIH).
    1965 Rinker, R. G., Lynn, S., Mason, D. M., Corcoran, W. H.: Kinetics and Mechanism of the Thermal Decomposition of Sodium Dithionite in Aqueous Solution, Ind. Eng. Chem. Fundmtls., vol. 4, 282–288CrossRefGoogle Scholar
  85. (IIIJ).
    1975 Rossler, O. E.: A Multivibrating Switching Network in Homogeneous Kinetics, Bull. Math. Biol., vol. 37, 181–192PubMedGoogle Scholar
  86. (IIIJ).
    1976-1 Rossler, O. E.: Chaotic Behavior in Simple Reaction Systems, Z. Naturforschung, vol. 31a, 259–264Google Scholar
  87. (IIIJ).
    1976-2 Rossler, O. E.: An Equation for Continuous Chaos Physics Letters, vol. 57a, 397–398CrossRefGoogle Scholar
  88. (IIIJ).
    1976-3 Rossler, O. E.: Chemical Turbulence: Chaos in a Simple Reaction-Diffusion System, Z. Naturforschung, vol. 31a, 1168–1172Google Scholar
  89. (IIIJ).
    1976-4 Rossler, O. E.: Different Types of Chaos in Two Differential Equations, Z. Naturforschung, vol. 31a, p. 1664–1670Google Scholar
  90. (IIIJ).
    1977-1 Rossler, O. E.: Toroidal Oscillation in a 3-Variable Abstract Reaction System, Z. Naturforsch., vol. 32a, 299–301Google Scholar
  91. (IIIJ).
    1977-2, 3 Rossler, O. E.: Chaos in Abstract Kinetics: Two Prototypes, Bull. Math. Biol., vol. 39, 275–289PubMedGoogle Scholar
  92. (IIIJ).
    1977-4, 5 Rossler, O. E.: Continuous Chaos, In: Synergetics: A Workshop, (H, Haken, ed.) Noted in Physics, Springer-Verlag, p. 184–199Google Scholar
  93. (IIIC).
    1978 Rossler, O. E., Wegmann, K.: Chaos in the Zhabotinskii Reaction, Nature, vol. 271, 89–90Google Scholar
  94. (IIIJ).
    1979-1 Rossler, O. E.: Continuous Chaos: Four Prototype Equations, In: Gurel and Rossler, (Book B4), 376–392Google Scholar
  95. (R13).
    1979-2 Rossler, O. E.: Chaos and Strange Attractors in Chemical Kinetics, Springer Series in Synergetics, vol. 3, 107–113Google Scholar
  96. (IIID).
    1948 Salnikov, I. E.: Thermodynamic Model of Homogeneous Periodic Reactions, (in Russian), Dokl. Akad. Nauk SSSR, vol. 60, 405–408Google Scholar
  97. (IIID).
    1949 Salnikov, I. E.: On the Theory of Periodic Course of Homogeneous Chemical Reactions, (in Russian), Zh. Fiz. Khim., vol. 23, 258–272Google Scholar
  98. (R7).
    1975 Schmitz, R. A.: Multiplicity, Stability and Sensitivity of States in Chemically Reacting Systems In: Chemical Reaction Engineering Reviews (ed. Hulburt, H. H.), Advances in Chemistry Series, 148. American Chemical Society, Washington, D.C., 156–211Google Scholar
  99. (IIIF).
    1978 Schulmeister, Th.: Chaos in a Lotka-Scheme with Depot, Studia Biophysica, vol. 72, 205–206Google Scholar
  100. (IIIF).
    1978 Schulmeister, Th., Sel'kov, E. E.: Folded Limit Cycles and Quasi-Stochastic Self-Oscillations in a Third Order Model of an Open Biochemical System, Studia Biophysica, vol. 72, 111–112Google Scholar
  101. (IIIF).
    1968-1 Sel'kov, E. E.: Self-Oscillations in Glycolysis. A Simple Kinetic Model, Eur. J. Biochem., vol. 4, 79–86Google Scholar
  102. (IIIF).
    1968-2 Sel'kov, E. E.: Self-Oscillations in Glycolysis. Simple Single-Frequency Model, Molecular Biology, vol. 2, 208–221 (Molekulyarnaya Biologiya 252–266)Google Scholar
  103. (IIIF).
    1972 Sel'kov, E. E.: Nonlinearity of Multienzyme Systems In: Analysis and Simulation of Biochemical Systems, (Hemker, H. C., Hess, B., eds.) FEBS 25, North-Holland, Amsterdam, 145–161Google Scholar
  104. (IIIF).
    1973 Sel'kov, E. E., Betz, A.: On the Mechanism of Single-Frequency Glycolytic Oscillations, In: Biological and Biochemical Oscillations, (Chance, et al. eds.) Academic Press, 197–220Google Scholar
  105. (IIIF).
    1979 Sel'kov, E. E., Dynnik, S. N., Kirsta, Y. B.: Qualitative Investigation of a Mathematical Model of the Open Futile Cycle of fructose-6-P → fructose-1,6-P2, Biophysics, vol. 24, 443–450 (Biofizika, 431–437)Google Scholar
  106. (IIIF).
    1980 Sel'kov, E. E.: Instability and Self-Oscillations in the Cell Energy Metabolism, Berichte der Bunsen-Gesellschaft für Physikalische Chemie, vol. 84, no. 4, 399–406Google Scholar
  107. (IIIA).
    1976 Sharma, K. R., Noyes, R. M.: Oscillations in Chemical Systems, 13. A Detailed Molecular Mechanism for the Bray-Liebhafsky Reaction of Iodate and Hydrogen Peroxide, J. Amer. Chem. Soc. vol. 98, 4345–4361Google Scholar
  108. (R10).
    1977 Sheintuch, M., Schmitz, R. A.: Oscillations in Catalytic Reaction, Catalysis Reviews, vol. 15, 107–172Google Scholar
  109. (III A).
    1911 Skrabal, A.: Zur Kenntnis der unterhalogenigen Säuren und der Hypohalogenite, V. Die Kinetik der Jodatbildung aus Iod und Hydroxylion, Monat. Chemie, vol. 32. 815–903CrossRefGoogle Scholar
  110. (III C).
    1915 Skrabal, A., Weberitsch, S. R.: Zur Kenntnis der Halogensauerstoffverbindungen, IX. Die Kinetik der Bromat-Bromidreaktion Monat. Chemie vol. 36, 211–235. X. Die Kinetik der Bromatbildung aus Brom Monat. Chemie vol. 36, 237–256Google Scholar
  111. (V2).
    1980 Tockstein, A., Komers, K.: Biomolecular Kinetic Scheme with a Stable and an Unstable Limit Cycle of Two Oscillatory Components Collection Czechoslovak Chem-Commun. vol. 45, 2135–2142Google Scholar
  112. (III D).
    1974 Uppal, A, Ray, W. H., Poore, A. B.: On the Dynamic Behavior of Continuous Stirred Tank Reactors, Chem. Eng. Sci. vol. 29, 967–985CrossRefGoogle Scholar
  113. (III D).
    1976 Uppal, A, Ray, W. H., Poore, A. B.: The Classification of the Dynamic Behavior of Continuous Stirred Tank Reactors-Influence of Reactor Residue Time Chem. Eng. Sci. vol. 31, 205–214CrossRefGoogle Scholar
  114. (III C).
    1973 Vavilin, V. A., Zhabotinskii, A. M., Zaikin, A. N.: A Study of a Self-Oscillatory Chemical Reaction, I. The Autonomous System, In: Biological and Biochemical Oscillations (Ed. B. Chance), 71–79Google Scholar
  115. (III C).
    1978 Wegmann, K., Rossler, O. E.: Different Kinds of Chaotic Oscillations in the Belousov-Zhabotinskii Reaction, Z. Naturforschung A, vol. 33A, no. 10, 1170–1183Google Scholar
  116. (III J).
    1980 Willamowski, Rossler, O. E.: Irregular Oscillations in a Realistic Abstract Quadratic Mass Action System, Z. Naturforsch., vol. 35a, 317–318Google Scholar
  117. (III G).
    1965 Yamazaki, L., Yokoya, K., Nakajima, R.: Oscillatory Oxidations of Reduced Pyridine Nucleotide by Peroxidase, Biochim. Biophys. Res. Commun., vol. 21, 582–586CrossRefGoogle Scholar
  118. (III G).
    1967 Yamazaki, I., Yokota, K.: Analysis of the Conditions Causing the Oscillatory Oxidation of Reduced Nicotinamide-Adenine Dinucleotide by Biochem. Biophys. Acta, vol. 132, 310–320Google Scholar
  119. (III E).
    1974 Yang, C. H.: On the Explosion, Glow and Oscillation Phenomena in the Oxidation of Carbon Monoxide, Combustion and Flame, vol. 23, 97–108Google Scholar
  120. (III C).
    1932 Young, H. A., Bray, W. C.: The Rate of the Fourth Order Reaction between Bromic and Hydrobromic Acid. The Kinetic Salt Effect. J. Amer. Chem. Soc., vol. 54, 4284–4296CrossRefGoogle Scholar
  121. (III C).
    1973 Zaikin, A. N., Zhabotinskii, A. M.: A Study of a Self-oscillatory Chemical Reaction, In: B. Chance, et al. (Book-B1) 81–88Google Scholar
  122. (III C).
    1964–1 Zhabotinskii, A. M.: Periodic Course of Oxidation of Malonic Acid in Solution, (An Investigation of the Kinetics of the Reaction of Belousov), Biophysics, vol. 9, 329–335, (Biofizika, 9, 306–311)Google Scholar
  123. (III C).
    1964–2 Zhabotinskii, A. M.: Periodic Oxidation Reaction in Liquid Phase, (in Russian) Dokl. Akad. Nauk SSSR vol. 157, no. 2, 392–395Google Scholar


  1. (B1).
    1973 Chance, B., Ghosh, A. K., Pye, E. K., Hess, B. (Eds.): Biological and Biochemical Oscillators, Academic Press, New York Academic Press, New YorkGoogle Scholar
  2. (B2).
    1974 Physical Chemistry of Oscillatory Phenomena, Symposia of the Faraday Society, no. 9, The Faraday Division, Chemical Society, LondonGoogle Scholar
  3. (B3).
    1979 Pacault, A., Vidal, C. (Eds.): Synergetics, Far from Equilibrium, Springer-Verlag Series in Synergetics, vol. 3, Springer, Berlin, Heidelberg, New YorkGoogle Scholar
  4. (B4).
    1979 Gurel, O., Rossler, O. E. (Eds.): Bifurcation Theory and Applications in Scientific Disciplines N.Y. Acad. of Sciences Annals no. 316Google Scholar

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© Springer-Verlag 1983

Authors and Affiliations

  • Okan Gurel
    • 1
  • Demet Gurel
    • 2
  1. 1.Cambridge Scientific CenterIBM CorporationCambridgeUSA
  2. 2.Department of ChemistryNew York UniversityNew YorkUSA

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