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A note on the existence of heteroclinic connecting orbits in the Belousov-Zhabotinskii system

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Abstract

We prove for a concrete system the occurence of heteroclinic orbits via the Conley index. Because this system is bistable, we have two different connecting orbits. If we include the parameter dependence of the reaction term, there exists two families of connecting orbits. At the ends of the parameter interval, where bistability occurs, we have bifurcation points.

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References

  1. R.C. Churchill, J. Diff. Equ. 12 (1952) 330.

    Google Scholar 

  2. Ch. Conley, Isolated invariant sets and the Morse index,Reg. Conf. Ser. Math. 38 (AMS, Providence, 1978).

    Google Scholar 

  3. R. Gardner, Rend. Ist. Mat. Univ. Trieste 18 (1986) 65.

    Google Scholar 

  4. M. Kem, H.-J. Krug and L. Pohlmann, J. Math. Chem. 6 (1991) 359.

    Google Scholar 

  5. M. Kem, On the existence of travelling waves in reaction-diffusion-systems and application to the Belousov-Zhabotinskii-reaction, Preprint, Berlin (1992).

  6. L. Kuhnert, H.-J. Krug and L. Pohlmann, J. Phys. Chem. 89 (1985) 2022.

    Google Scholar 

  7. L. Kuhnert, L. Pohlmann, H.-J. Krug and G. Wesslerg, in:Selforganization by Nonlinear Irreversible Processes, eds. W. Ebeling and H. Ulbricht (Springer, Berlin, 1986).

    Google Scholar 

  8. L. Kuhnert and H.-J. Krug, J. Phys. Chem. 91 (1987) 730.

    Google Scholar 

  9. L. Kuhnert, L. Pohlmann and H.-J. Krug, Physica D29 (1988) 416.

    Google Scholar 

  10. K. Mischaikow, J. Diff. Equ. 81 (1989) 167.

    Google Scholar 

  11. J. Reineck, Trans. Amer. Soc. 307 (1988) 535.

    Google Scholar 

  12. J. Smoller,Shock Waves and Reaction-Diffusion Equations (Springer, New York, Berlin, 1983).

    Google Scholar 

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Author notes

  1. Marietta Kern

    Present address: Fachhochschule Lippe, Fachbereich Elektrotechnik, Liebigstraße 87, D-32657, Lemgo, Germany

Authors and Affiliations

  1. Department ofApplied Mathematics, Technical University of Gdansk, ul. Majakowskiego 11/12, 80-952, Gdansk, Poland

    Marek Izydorek & Stawomir Rybicki

  2. Institute of Applied Analysis and Stochastics, Mohrenstraße 39, 1086, Berlin, Germany

    Marietta Kern

Authors
  1. Marek Izydorek
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  2. Stawomir Rybicki
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  3. Marietta Kern
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Izydorek, M., Rybicki, S. & Kern, M. A note on the existence of heteroclinic connecting orbits in the Belousov-Zhabotinskii system. J Math Chem 15, 115–121 (1994). https://doi.org/10.1007/BF01277553

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  • DOI: https://doi.org/10.1007/BF01277553

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