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The mechanism of bursting phenomena in Belousov-Zhabotinsky (BZ) chemical reaction with multiple time scales

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Abstract

The dynamics of a typical Belousov-Zhabotinsky (BZ) reaction with multiple time scales is investigated in this paper. Different forms of periodic bursting phenomena, and specially, three types of chaotic bursters with different structures can be obtained, which are in common with the behaviors observed in experiments. The bifurcations connecting the quiescent state and the repetitive spikes are presented to account for the occurrence of the N K oscillations as well as the different forms of chaotic bursters. The mechanism of the period-adding bifurcation sequences is explored to reveal why the length of the periods in the sequences does not change continuously with the continuous variation of the parameters.

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References

  1. Neugebauer J, Zywietz T, Scheffler M, et al. Adatom kinetics on and below the surface: The existence of a new diffusion channel. Phys Rev Lett, 2003, 90: 056101

    Article  Google Scholar 

  2. Passerone D, Parrinello M. Action-derived molecular dynamics in the study of rare event. Phys Rev Lett, 2001, 87: 108302

    Article  Google Scholar 

  3. Davis M J, Klippenstein S J. Geometric investigation of association/dissociation kinetics with an application to master equation for CH 3+CH 3 ↔ C 2 H 3. J Phys Chem A, 002, 106: 5860–5879

  4. Mease K D. Multiple time-scales in nonlinear flight mechanics: diagnosis and modeling. Appl Math Comput, 2005, 164: 627–648

    Article  MATH  MathSciNet  Google Scholar 

  5. Field R J, Gyorgyi L. Chaos in Chemistry and Biochemistry, Singapore: World Scientific, 1993

    Google Scholar 

  6. Gyorgyi L, Field R J. A three-variable model of deterministic chaos in the Belousov-Zhabotinsky reaction. Nature, 1992, 355: 808–810

    Article  Google Scholar 

  7. Snydera J S, Large E W. Tempo dependence of middle- and long-latency auditory responses: power and phase modulation of the EEG at multiple time-scales. Clinical Neurophysiol, 2004, 115: 1885–1895

    Article  Google Scholar 

  8. Rajesh S, Ananthakrishna G. Relaxation oscillations and negative strain rate sensitivity in the portevin-Le Chatelier effect. Phys Rev E, 2000, 61: 3664–3669

    Article  Google Scholar 

  9. Raghavan R, Ananthakrishna G. Long tailed maps as a representation of mixed mode oscillatory systems. Phys D, 2005, 211: 74–87

    Article  MATH  MathSciNet  Google Scholar 

  10. Bier M, Bountis T C. Remerging Feigenbaum trees in dynamical systems. Phys Lett A, 1984, 104: 239–244

    Article  MathSciNet  Google Scholar 

  11. Li Q S, Zhu R. Chaos to periodicity and periodicity to chaos by periodic perturbations in the Belousov-Zhabotinsky reaction. Chaos, Solitons and Fractals, 2004, 19:195–201

    Article  MathSciNet  Google Scholar 

  12. Izhikevich E M. Neural excitablitity, spiking and bursting. Int J Bifur Chaos, 2002, 10: 1171–1266

    Article  MathSciNet  Google Scholar 

  13. Rosenblum M G., Pikovsky A S, Kurths J. Phase synchronization of chaotic oscillators. Phys Rev Lett, 1996, 76: 1804–1807

    Article  Google Scholar 

  14. Guckenheimer J, Holmes P. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. New York: Springer-Verlag, 1983

    MATH  Google Scholar 

  15. Savino G V, Formigli C M. Nonlinear electronic circuit with neuron like bursting and spiking dynamics. Biosystems, 2009, 97: 9–14

    Article  Google Scholar 

  16. Perc M, Marhl M. Resonance effects determine the frequency of bursting Ca 2+ oscillations. Chem Phys Lett, 2003, 376: 432–437

    Article  Google Scholar 

  17. Surana A, Haller G. Ghost manifolds in slow fast systems with applications to unsteady fluid flow separation. Phys D, 2008, 237: 1507–1529.

    Article  MATH  MathSciNet  Google Scholar 

  18. Fridman E. Exact slow-fast decomposition of the nonlinear singularly perturbed optimal control problem. Systems Control Lett, 2000, 40: 121–131

    Article  MATH  MathSciNet  Google Scholar 

  19. Fujimoto F, Kaneko K. How fast elements can affect slow dynamics. Phys D, 2003, 180: 1–16

    Article  MATH  MathSciNet  Google Scholar 

  20. Conforto F, Groppi M, Jannelli A. On shock solutions to balance equations for slow and fast chemical reaction. Appl Math Comput, 2008, 206: 892–905

    Article  MATH  MathSciNet  Google Scholar 

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  1. Faculty of Science, Jiangsu University, Zhenjiang, 212013, China

    QinSheng Bi

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  1. QinSheng Bi
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Correspondence to QinSheng Bi.

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Bi, Q. The mechanism of bursting phenomena in Belousov-Zhabotinsky (BZ) chemical reaction with multiple time scales. Sci. China Technol. Sci. 53, 748–760 (2010). https://doi.org/10.1007/s11431-010-0082-8

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  • DOI: https://doi.org/10.1007/s11431-010-0082-8

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