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A Spatial Frequency Domain Analysis of the Belousov–Zhabotinsky Reaction

Lingzhong Guo

Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, S1 3JD, UK

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Yuzhu Guo

Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, S1 3JD, UK

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Yifan Zhao

Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, S1 3JD, UK

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Stephen A. Billings

Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, S1 3JD, UK

Author for correspondence.

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Daniel Coca

Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, S1 3JD, UK

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, and

Zhiqiang Lang

Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, S1 3JD, UK

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https://doi.org/10.1142/S021812741450031XCited by:2 (Source: Crossref)

Abstract

A nonlinear spatio-temporal system identification and analysis approach is used to study the dynamical behavior of the Belousov–Zhabotinsky (BZ) chemical reaction process. In our previous study [Guo et al., 2010],, the dynamical behavior of the BZ reaction in the spatial-temporal domain has been analyzed by identifying a coupled map lattice (CML) model of the process directly from experimental data from a real BZ reaction experiment. In this paper, the frequency domain analysis of the dynamics near equilibrium is carried out by mapping the obtained CML model into higher order spatial frequency response functions to reveal the nonlinear coupling and modulation between the various initial spectral components in the process. As far as we are aware, this is the first study of any real spatio-temporal system using a spatio-temporal domain identification and frequency domain analysis approach.

Keywords:

References

B. P. Belousov , A Periodic Reaction and Its Mechanism ( Sbornik Referatov po Radiasionni Meditsine , Moscow , 1958 ) . Google Scholar
S. A. Billings and K. M. Tsang, Mech. Syst. Sign. Process. 3, 319 (1989), DOI: 10.1016/0888-3270(89)90041-1. Crossref, Web of Science, Google Scholar
S. A. Billings and K. M. Tsang, Mech. Syst. Sign. Process. 3, 341 (1989), DOI: 10.1016/0888-3270(89)90042-3. Crossref, Web of Science, Google Scholar
S. A. Billings and J. C. Peyton-Jones, Int. J. Contr. 52, 863 (1990), DOI: 10.1080/00207179008953572. Crossref, Web of Science, Google Scholar
S. A. Billings and D. Coca, Int. J. Syst. Sci. 33, 623 (2002), DOI: 10.1080/00207720210147106. Crossref, Web of Science, Google Scholar
S. A. Billings , Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains ( Wiley , UK , 2013 ) . Crossref, Google Scholar
M. H. Chou, H. C. Wei and Y. T. Lin, Int. J. Bifurcation and Chaos 17, 4337 (2007), DOI: 10.1142/S0218127407019998. Link, Web of Science, Google Scholar
D. Coca and S. A. Billings, Phys. Lett. A 287, 65 (2001), DOI: 10.1016/S0375-9601(01)00136-0. Crossref, Web of Science, Google Scholar
D. Coca and S. A. Billings, Automatica 38, 1851 (2002), DOI: 10.1016/S0005-1098(02)00099-7. Crossref, Web of Science, Google Scholar
R. Field and R. Noyes, J. Chem. Phys. 60, 1877 (1974), DOI: 10.1063/1.1681288. Crossref, Web of Science, Google Scholar
R. FitzHugh, Bull. Math. Biol. 17, 257 (1955). Google Scholar
P. Glansdorff and I. Prigogine , Thermodynamic Theory of Structure, Stability and Fluctuations ( Wiley Interscience , NY , 1971 ) . Google Scholar
P. Gray and S. K. Scott, Chem. Engin. Sci. 38, 29 (1983), DOI: 10.1016/0009-2509(83)80132-8. Crossref, Web of Science, Google Scholar
Y. Z. Guoet al., Int. J. Bifurcation and Chaos 20, 2137 (2010), DOI: 10.1142/S0218127410026976. Link, Web of Science, Google Scholar
L. Z. Guoet al., Syst. Contr. Lett. 62, 115 (2013), DOI: 10.1016/j.sysconle.2012.11.011. Crossref, Web of Science, Google Scholar
J. C. Peyton-Jones and S. A. Billings, Int. J. Contr. 50, 1925 (1989). Crossref, Web of Science, Google Scholar
M. Schetzen , The Volterra and Wiener Theories of Nonlinear Systems ( John Wiley , Chichester , 1980 ) . Google Scholar
A. M. Turing, Phil. Trans. Roy. Soc. B 237, 37 (1952), DOI: 10.1098/rstb.1952.0012. Crossref, Web of Science, Google Scholar
K. Worden, G. Manson and G. R. Tomlinson, J. Sound Vibr. 201, 67 (1997), DOI: 10.1006/jsvi.1996.0746. Crossref, Web of Science, Google Scholar
A. M. Zhabotinsky, Biofizika 9, 306 (1964). Google Scholar
Y. F. Zhao, S. A. Billings and A. F. Routh, Int. J. Bifurcation and Chaos 17, 1687 (2007), DOI: 10.1142/S0218127407017999. Link, Web of Science, Google Scholar
Y. F. Zhaoet al., Int. J. Bifurcation and Chaos 21, 3249 (2011), DOI: 10.1142/S0218127411030490. Link, Web of Science, Google Scholar