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Chaos of a coupled lattice system related with the Belusov–Zhabotinskii reaction

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Abstract

In this paper we present a lattice dynamical system stated by Kaneko in (Phys Rev Lett, 65: 1391–1394, 1990) which is related to the Belusov–Zhabotinskii chemical reaction. We prove that this CML (Coupled Map Lattice) system is chaotic in the sense of Li–Yorke and in the sense of Devaney for zero coupling constant. Some problems on the dynamics of this system are stated for the case of having non-zero coupling constant.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Hospital de Marina, 30203, Cartagena (Región de Murcia), Spain

    Juan Luis García Guirao

  2. Department of Applied Mathematics, VŠB–Technical University of Ostrava, 17. listopadu 15/2172, 708 33, Ostrava, Czech Republic

    Marek Lampart

Authors
  1. Juan Luis García Guirao
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  2. Marek Lampart
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Corresponding author

Correspondence to Juan Luis García Guirao.

Additional information

This research was supported in part by MEC (Ministerio de Educación y Ciencia, Spain) grants MTM2005-03860 and MTM2005-06098-C02-01; Fundación Séneca (Comunidad Autónoma de la Región de Murcia), grant 00684-FI-04, by Grant Agency of the Czech Republic grant 201/07/P032, Ministry of Education of the Czech Republic No. MSM6198910027 and VaV 1/09 of the Moravian-Silesian Region of the Czech Republic.

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Guirao, J.L.G., Lampart, M. Chaos of a coupled lattice system related with the Belusov–Zhabotinskii reaction. J Math Chem 48, 159–164 (2010). https://doi.org/10.1007/s10910-009-9647-9

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  • DOI: https://doi.org/10.1007/s10910-009-9647-9

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