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On the study of nonlinear dynamics of complex chemical reaction systems

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Abstract

With ever-increasing attentions being paid to complex systems such as the life system, soft matter, and nano-systems, theoretical studies of non-equilibrium nonlinear problems involved in chemical dynamics are now of general interest. In this mini-review, we mainly give a brief introduction to some frontier topics in this field, namely, nonlinear state-state dynamics, nonlinear chemical dynamics on complex networks, and nonlinear dynamics in mesoscopic chemical reaction systems. Deep study of these topics will make great contribution to discovering new laws of chemical dynamics, to exploring new control methods of complex chemical processes, to figuring out the very roles of chemical processes in the life system, and to crosslinking the scientific study of chemistry, physics and biology.

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References

  1. Xin, H. W., Nonlinear Chemistry (in Chinese), Hefei: University of Science and Technology Press, 1999, 1–34.

    Google Scholar 

  2. Elowitz, M. B., Leibler, S., A synthetic oscillatory network of transcriptional regulators, Nature, 2000, 403(6767): 335–338.

    Article  CAS  Google Scholar 

  3. Berridge, M. J., Bootman, M. D., Lipp, P., Calcium—A life and death signal, Nature, 1998, 395(6703): 645–648.

    Article  CAS  Google Scholar 

  4. Imbihl, R., Ertl, G., Oscillatory kinetics in heterogeneous catalysis, Chem. Rev., 1995, 95(3): 697–733.

    Article  CAS  Google Scholar 

  5. Kim, M., Bertram, M., Pollmann, M. et al., Controlling chemical turbulence by global delayed feedback: Pattern formation in catalytic CO oxidation on Pt(110), Science, 2001, 292(5520): 1357–1360.

    Article  CAS  Google Scholar 

  6. Vanag, V. K., Epstein, I. R., Segmented spiral waves in a reaction-diffusion system, Proc. Natl. Acad. Sci. USA, 2003, 100(25): 14635–14638.

    Article  CAS  Google Scholar 

  7. Dafilis, M. P., Liley, D. T. J., Cadusch, P. J., Robust chaos in a model of the electroencephalogram: Implications for brain dynamics, Chaos, 2001, 11(3): 474–478.

    Article  Google Scholar 

  8. Nicolis, G., Prigogine, I., Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order Through Fluctuations, New York: John Wiley & Sons Inc., 1977.

    Google Scholar 

  9. Gammaitoni, L., Hänggi, P., Jung, P. et al., Stochastic resonance, Rev. Mod. Phys., 1998, 70(1): 223–287.

    Article  CAS  Google Scholar 

  10. Hänggi, P., Stochastic resonance in biology: How noise can enhance detection of weak signals and help improve biological information processing, ChemPhysChem, 2002, 3(3): 285–290.

    Google Scholar 

  11. Benzi, R., Parisi, G., Sutera, A. et al., The mechanism of stochastic resonance, J. Phys. A: Math. Gen, 1981, 14(11): L453–L457.

    Article  Google Scholar 

  12. Guderian, A., Dechert, G., Zeyer, K. P. et al., Stochastic resonance in chemistry, 1. The Belousov-Zhabotinsky reaction, J. Phys. Chem., 1996, 100(11): 4437–4441.

    Article  CAS  Google Scholar 

  13. Forster, A., Merget, M., Schneider, F. W., Stochastic resonance in chemistry, 2. The peroxidase-oxidase reaction, J. Phys. Chem., 1996, 100(11): 4442–4447.

    Article  Google Scholar 

  14. Yang, L. F., Hou, Z. H., Xin, H. W., Stochastic resonance in surface catalytic oxidation of carbon monoxide, J. Chem. Phys., 1998, 109(5): 2002–2005.

    Article  CAS  Google Scholar 

  15. Yang, L. F., Hou, Z. H., Xin, H. W. et al., Stochastic resonance in catalytic reduction of NO with CO on Pt(100), J. Chem. Phys., 1998, 109(15): 6456–6459.

    Article  CAS  Google Scholar 

  16. Zuo, X. B., Hou, Z. H., Xin, H. W., Stochastic resonance in liquid membrane oscillator, J. Chem. Phys., 1998, 109(14): 6063–6066.

    Article  CAS  Google Scholar 

  17. Hou, Z. H., Xin, H. W., Noise-induced oscillation and stochastic resonance in an autonomous chemical reaction system, Phys. Rev. E, 1999, 60(6): 6329–6332.

    Article  CAS  Google Scholar 

  18. Hou, Z. H., Xin, H. W., Stochastic resonance in the presence or absence of external signal in the continuous stirred tank reactor system, J. Chem. Phys., 1999, 111(2): 721–723.

    Article  CAS  Google Scholar 

  19. Hou, Z. H., Xin, H. W., Stochastic bi-resonance without external signal in the CO+O-2 catalytic oxidation reaction system, J. Chem. Phys., 1999, 111(4): 1592–1594.

    Article  CAS  Google Scholar 

  20. Zhong, S., Qi, F., Xin, H. W., Internal stochastic resonance in a model system for intracellular calcium oscillations, Chem. Phys. Lett., 2001, 342(5-6): 583–586.

    Article  CAS  Google Scholar 

  21. Wang, Z. W., Hou, Z. H., Xin, H. W., Noise-enhanced energy transduction of molecular machinery, Chem. Phys. Lett., 2002, 362(1-2): 51–55.

    CAS  Google Scholar 

  22. Wang, Z. W., Hou, Z. H., Xin, H. W., Internal noise stochastic resonance of synthetic gene network, Chem. Phys. Lett., 2005, 401(1-3): 307–311.

    Article  CAS  Google Scholar 

  23. Jiang, Y. J., Zhong, S., Xin, H. W., Experimental observation of internal signal stochastic resonance in the Belousov-Zhabotinsky reaction, J. Phys. Chem. A, 2001, 104(37): 8521–8523.

    Google Scholar 

  24. Manjarrez, E., Rojas-Piloni, J. G., Mendez, I. et al., Internal stochastic resonance in the coherence between spinal and cortical neuronal ensembles in the cat, Neurosci. Lett., 2002, 326(2): 93–96.

    Article  CAS  Google Scholar 

  25. Hou, Z. H., Yang, L. F., Xin, H. W., Noise induced pattern transition and spatiotemporal stochastic resonance, Phys. Rev. Lett., 1998, 81(14): 2854–2857.

    CAS  Google Scholar 

  26. Hou, Z. H., Xin, H. W., Noise-sustained spiral waves: Effect of spatial and temporal memory, Phys. Rev. Lett., 2002, 89(28): 280601.

    Google Scholar 

  27. Watts, D. J., Strogatz, S. H., Collective dynamics of ’small-World’ networks, Nature, 1998, 393(6684): 440–442.

    Article  CAS  Google Scholar 

  28. Barabasi, A. L., Albert, R., Emergence of scaling in random networks, Science, 1999, 286(5439): 509–512.

    Google Scholar 

  29. Collins, J. J., Chow, C. C., It’s a small world, Nature, 1998, 393(6684): 409–410.

    Article  CAS  Google Scholar 

  30. Albert, R., Barabasi, A. L., Statistical mechanics of complex networks, Rev. Mod. Phys, 2002, 74(1): 47–97.

    Article  Google Scholar 

  31. Strogatz, S. H., Exploring complex networks, Nature, 2001, 410(6825): 268–276.

    Article  CAS  Google Scholar 

  32. Qi, F., Hou, Z. H., Xin, H. W., Ordering chaos by random shortcuts, Phys. Rev. Lett., 2003, 91(6): 064102.

    Google Scholar 

  33. Hou, Z. H., Xin, H. W., Oscillator death on small-world networks, Phys. Rev. E, 2003, 68(5): 055103R.

    Google Scholar 

  34. Gong, Y. B., Hou, Z. H., Xin, H. W., Optimal spike coherence and synchronization on complex Hodgkin-Huxley neuron networks, ChemPhysChem, 2005, 6: 1042–1047.

    Article  CAS  Google Scholar 

  35. McAdams, H. H., Arkin, A., It’s a noisy business, Trend. Genet, 1999, 15(2): 65–69.

    CAS  Google Scholar 

  36. Swain, P. S., Elowitz, M. B., Siggia, E. D., Intrinsic and extrinsic contributions to stochasticity in gene expression, Proc. Natl. Acad. Sci. USA, 2002, 99(20): 12795–12800.

    Article  CAS  Google Scholar 

  37. Elowitz, M. B., Levine, A. J., Siggia, E. D. et al., Stochastic gene expression in a single cell, Science, 2002, 297(5584): 1183–1186.

    Article  CAS  Google Scholar 

  38. Paulsson, J., Summing up the noise in gene networks, Nature, 2004, 427(6973): 415–418.

    Article  CAS  Google Scholar 

  39. Rao, C. V., Wolf, D. M., Arkin, A., Control, exploitation and tolerance of intracellular noise, Nature, 2002, 420(6912): 231–237.

    Article  CAS  Google Scholar 

  40. Thattai, M., Oudenaarden, A. V., Intrinsic noise in gene regulatory networks, Proc. Natl. Acad. Sci. USA, 2001, 98(15): 8614–8619.

    Article  CAS  Google Scholar 

  41. McAdams, H. H., Adam, A., Stochastic mechanisms in gene expression, Proc. Natl. Acad. Sci. USA, 1997, 94(3): 814–819.

    Article  CAS  Google Scholar 

  42. Hasty, J., Collins, J. J., Translating the noise, Nature Genetics, 2002, 31(3): 13–14.

    CAS  Google Scholar 

  43. Blake, W. J., Kærn, M., Cantor, C. R. et al., Noise in eukaryotic gene expression, Nature, 2003, 422(6932): 633–637.

    Article  CAS  Google Scholar 

  44. Suchorski, Y., Beben, J., James, E. W. et al., Fluctuation-induced transitions in a bistable surface reaction: Catalytic CO oxidation on a Pt field emitter tip, Phys. Rev. Lett., 1999, 82(9): 1907–1910.

    Article  CAS  Google Scholar 

  45. Sachs, C., Hildebrand, M., Volkening, S. et al., Spatio-temporal self-organization in a surface reaction: From the atomic to the mesoscopic scale, Science, 2001, 293(5535): 1635–1638.

    Article  CAS  Google Scholar 

  46. Slin’ko, M. M., Ukharskii, A. A., Peskov, N. V. et al., Chaos and synchronisation in heterogeneous catalytic systems: CO oxidation over Pd zeolite catalysts, Catal. Today, 2001, 70(4): 341–357.

    CAS  Google Scholar 

  47. Peskov, N. V., Slinko, M. M., Jaeger, N. I., Stochastic model of reaction rate oscillations in the CO oxidation on nm-sized palladium particles, J. Chem. Phys., 2002, 116(5): 2098–2106.

    Article  CAS  Google Scholar 

  48. Gong, Y. B., Hou, Z. H., Xin, H. W., Optimal particle size for reaction rate oscillation in CO oxidation on nm-sized palladium particles, J. Phys. Chem. B, 2004, 108(46): 17796–17799.

    Article  CAS  Google Scholar 

  49. Hou, Z. H., Xin, H. W., Internal noise stochastic resonance in a circadian clock system, J. Chem. Phys, 2003, 119(22): 11508–11512.

    Article  CAS  Google Scholar 

  50. Hou, Z. H., Xin, H. W., Optimal system size for mesoscopic chemical oscillations, ChemPhysChem, 2004, 5(3): 407–410.

    Article  CAS  Google Scholar 

  51. Zhang, J. Q., Hou, Z. H., Xin, H. W., System size bi-resonance for intracellular calcium signaling, ChemPhysChem, 2004, 5(7): 1041–1045.

    CAS  Google Scholar 

  52. Hou, Z. H., Rao, T., Xin, H. W., Effects of internal noise for rate oscillations during CO oxidation on platinum surfaces, J. Chem. Phys., 2005, 122(13): 134708.

    Google Scholar 

  53. Wang, M. S., Hou, Z. H., Xin, H. W., Double-system-size resonance for spiking activity of coupled Hodgkin-Huxley neurons, ChemPhysChem, 2004, 5(10): 1602–1605.

    CAS  Google Scholar 

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Correspondence to Xin Houwen.

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This review was recommended by Prof. Li Lemin, member of editorial board of Science in China.

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Xin, H., Hou, Z. On the study of nonlinear dynamics of complex chemical reaction systems. SCI CHINA SER B 49, 1–11 (2006). https://doi.org/10.1007/s11426-005-0077-7

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  • DOI: https://doi.org/10.1007/s11426-005-0077-7

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