Mixed-mode oscillations in a homogeneous pH-oscillatory chemical reaction system

Chaos

Volumn 18, Issue 1, 2008, Pages

  Bakeš, Daniel ^a   Schreiberová, Lenka ^a   Schreiber, Igor ^a   Hauser, Marcus J B ^b  

^a Ctr Nonlinear Dynam Chem Biol S   (Czech Republic)

^b OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 41549151996     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2779857     Document Type: Article

References (58)

1. W. Ostwald, Z. Phys. Chem. 35, 33 (1900). 0942-9352
2. R. A. Schmitz, K. R. Graziani, and J. L. Hudson, J. Chem. Phys. 0021-9606 10.1063/1.435267 67, 3040 (1977).
3. J. Maselko and H. L. Swinney, J. Chem. Phys. 0021-9606 10.1063/1.451473 85, 6430 (1986).
4. J. L. Hudson, M. Hart, and D. Marinko, J. Chem. Phys. 0021-9606 10.1063/1.438487 71, 1601 (1979).
5. K. Showalter, R. M. Noyes, and K. Bar-Eli, J. Chem. Phys. 0021-9606 10.1063/1.436894 69, 2514 (1978).
6. M. J. B. Hauser and L. F. Olsen, J. Chem. Soc., Faraday Trans. 0956-5000 10.1039/ft9969202857 92, 2857 (1996).
7. C. G. Steinmetz and R. Larter, J. Chem. Phys. 0021-9606 10.1063/1.459996 94, 1388 (1991).
8. T. Hauck and F. W. Schneider, J. Phys. Chem. 0022-3654 10.1021/j100104a021 97, 391 (1993).
9. X. J. Wang and J. Rinzel, in The Handbook of Brain Theory and Neural Networks, edited by, M. Arbib, (MIT Press, Cambridge, MA, 1995).
10. L. Glass and M. C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, NJ, 1988).
11. L. Brusch, W. Lorenz, M. Or-Guil, M. Bär, and U. Kummer, Z. Phys. Chem. 216, 487 (2002). 0942-9352
12. M. Falcke and D. Malchow, Understanding Calcium Dynamics (Springer, Berlin, 2003).
13. P. M. Dean and E. K. Mathews, J. Physiol. 210, 255 (1970). 0022-3751
14. K. Wierschem and R. Bertram, J. Theor. Biol. 0022-5193 10.1016/j.jtbi.2004.02.022 228, 513 (2004).
15. A. Goldbeter, Biochemical Oscillations and Cellular Rhythms (Cambridge University Press, Cambridge, UK, 1996).
16. C. J. Dixon, N. M. Woods, K. S. R. Cuthbertson, and P. H. Cobbold, Biochem. J. 269, 499 (1990). 0264-6021
17. N. M. Woods, K. S. R. Cuthbertson, and P. H. Cobbold, Nature (London) 0028-0836 10.1038/319600a0 319, 600 (1986).
18. J. Rinzel and G. B. Ermentrout, in Methods in Neuronal Modeling: From Synapses to Networks, edited by, C. Koch, and, I. Segev, (MIT Press, Cambridge, MA, 1989), p. 135.
19. E. M. Izhikevich, Int. J. Bifurcation Chaos Appl. Sci. Eng. 0218-1274 10.1142/S0218127400000840 10, 1171 (2000).
20. M. J. B. Hauser, L. F. Olsen, T. V. Bronnikova, and W. M. Schaffer, J. Phys. Chem. B 1089-5647 10.1021/jp9707549 101, 5075 (1997).
21. D. Barkley, J. Ringland, and J. S. Turner, J. Chem. Phys. 0021-9606 10.1063/1.452937 87, 3812 (1987).
22. O. V. Noskov, A. D. Karavaev, V. P. Kazakov, and S. I. Spivak, Mendeleev Commun. 0959-9436 10.1070/mc1997v007n01ABEH000649 7, 27 (1997).
23. A. Sensse, M. J. B. Hauser, and M. Eiswirth, J. Chem. Phys. 0021-9606 10.1063/1.2207140 125, 014901 (2006).
24. M. T. M. Koper, Physica D 0167-2789 10.1016/0167-2789(94)00171-L 80, 72 (1995).
25. J. Ringland, N. Issa, and M. Schell, Phys. Rev. A 1050-2947 10.1103/PhysRevA.41.4223 41, 4223 (1990).
26. J. Boissonade and P. DeKepper, J. Phys. Chem. 0022-3654 10.1021/j100442a009 84, 501 (1980).
27. A. Goryachev, P. Strizhak, and R. Kapral, J. Chem. Phys. 0021-9606 10.1063/1.474647 107, 2881 (1997).
28. G. Rábai, K. Kustin, and I. R. Epstein, J. Am. Chem. Soc. 0002-7863 10.1021/ja00193a018 111, 3870 (1989).
29. G. Rábai, R. Orban, and I. R. Epstein, J. Phys. Chem. 0022-3654 10.1021/j100192a043 96, 5414 (1992).
30. G. Rábai, A. Kaminaga, and I. Hanazaki, Chem. Commun. 18, 2181 (1996). 1364-548X
31. G. Rábai, J. Phys. Chem. A 1089-5639 10.1021/jp970970h 101, 7085 (1997).
32. G. A. Frerichs and R. C. Thompson, J. Phys. Chem. A 1089-5639 10.1021/jp983070p 102, 8142 (1998).
33. M. J. B. Hauser, A. Strich, R. Bakos, Zs. Nagy-Ungvárai, and S. C. Müller, Faraday Discuss. 0301-7249 10.1039/b105707n 120, 229 (2001).
34. R. Straube, S. C. Müller, and M. J. B. Hauser, Z. Phys. Chem. 0942-9352 10.1524/zpch.217.11.1427.20485 217, 1427 (2003).
35. G. Rábai and I. Hanazaki, J. Phys. Chem. A 1089-5639 10.1021/jp991600r 103, 7268 (1999).
36. R. Straube, D. Flockerzi, S. C. Müller, and M. J. B. Hauser, Phys. Rev. E 1063-651X 10.1103/PhysRevE.72.066205 72, 066205 (2005).
37. R. Straube, D. Flockerzi, and M. J. B. Hauser, J. Phys.: Conf. Ser. 1742-6588 10.1088/1742-6596/55/1/020 55, 214 (2006).
38. B. Hess, A. Boiteux, and J. Krüger, Adv. Enzyme Regul. 7, 149 (1969). 0065-2571
39. A. Naparstek, D. Thomas, and S. R. Kaplan, Biochim. Biophys. Acta 0006-3002 10.1016/0005-2736(73)90176-4 323, 643 (1973).
40. P. Masson, B. N. Goldstein, J. -C. Debouzy, M. T. Froment, O. Lockridge, and L. M. Schopfer, Eur. J. Biochem. 217, 220 (2003). 0014-2956
41. A. P. Dhanarajan, G. P. Misra, and R. A. Siegel, J. Phys. Chem. A 1089-5639 10.1021/jp026086v 106, 8835 (2002).
42. G. Baier, P. Strasser, and U. Kummer, Z. Naturforsch., A: Phys. Sci. 50, 1147 (1995).
43. M. Orbán and I. R. Epstein, J. Am. Chem. Soc. 0002-7863 10.1021/ja00235a017 109, 101 (1987).
44. D. Bakeš, L. Schreiberová, I. Schreiber, and M. J. B. Hauser, Russ. J. Phys. Chem. 0036-0244 10.1134/S0036024407090117 81, 1407 (2007).
45. K. Kurin-Csörgei, M. Orbán, G. Rábai, and I. R. Epstein, J. Chem. Soc., Faraday Trans. 92, 2851 (1996). 0956-5000
46. M. Orbán, K. Kurin-Csörgei, G. Rábai, and I. R. Epstein, Chem. Eng. Sci. 55, 267 (2000). 0009-2509
47. M. Vosla, P. Matějka, and I. Schreiber, Inorg. Chem. 45, 2824 (2006). 0020-1669
48. F. Takens, in Dynamical Systems and Turbulence, Lecture Notes in Mathematics Vol. 898, edited by, D. A. Rand, and, L. -S. Young, (Springer, Berlin, 1981), p. 366.
49. R. Hegger, H. Kantz, and T. Schreiber, Chaos 1054-1500 10.1063/1.166424 9, 413 (1999).
50. D. Broomhead and G. P. King, Physica D 0167-2789 10.1016/0167-2789(86) 90031-X 20, 217 (1986).
51. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, Physica D 0167-2789 10.1016/0167-2789(85)90011-9 16, 285 (1985).
52. H. Kantz, Phys. Lett. A 0375-9601 10.1016/0375-9601(94)90991-1 185, 77 (1994).
53. M. Menzinger and A. K. Dutt, J. Phys. Chem. 0022-3654 10.1021/j100374a031 94, 4510 (1990).
54. M. J. B. Hauser, D. Lebender, and F. W. Schneider, J. Phys. Chem. 96, 9332 (1992). 0022-3654
55. M. Brøns, M. Krupa, and M. Wechselberger, in Bifurcation Theory and Spatio-Temporal Pattern Formation, edited by, W. Nagata, and, N. Sri Namachchivaya, AMS/Fields Institute Communications (Oxford University Press, Oxford, 2006), p. 39.
56. A. Milik, P. Szmolyan, E. Gröller, and H. Löffelmann, Int. J. Bifurcation Chaos Appl. Sci. Eng. 0218-1274 10.1142/S0218127498000322 8, 505 (1998).
57. H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, Rev. Mod. Phys. 0034-6861 10.1103/RevModPhys.65.1331 65, 1331 (1993).
58. J. Keener and J. Sneyd, Mathematical Physiology (Springer, New York, 1998).