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Bifurcations in a system of two identical diffusion-coupled relaxational brusselators

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Abstract

We propose a two-parameter bifurcation analysis of the dynamics of a system of two identical asymmetrically coupled Brusselators. The stability boundaries of the inhomogeneous steady states and periodic attractors are calculated as the functions of the constraint force and one of the free parameters. The coexistence of different attractors giving rise to multirhythmicity of the dynamics is studied as well as the bifurcation transitions between them. It is shown that the relaxation ability of an oscillator plays an important role in the simplification of the phase diagram, since it removes the overlapping of the existence region for different solutions. We assume that the results primarily characterize the properties of the diffusion coupling and, therefore, they can be applied in the study of other oscillator systems.

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References

  1. I. Prigogine and R. Lefever,J. Chem. Phys.,48, 1695 (1968).

    Google Scholar 

  2. J. Tyson and S. Kauffman,J. Math. Biol.,1, 289 (1975).

    Google Scholar 

  3. J. Honerkamp,J. Math. Biol.,18, 69 (1983).

    Google Scholar 

  4. D. A. Linkens,Bull. Math. Biol.,39, 359 (1977).

    Google Scholar 

  5. K. Bar-Eli,J. Phys. Chem.,88, 3616, 6174 (1984).

    Google Scholar 

  6. K. Bar-Eli,J. Phys. Chem.,14, 242 (1985).

    Google Scholar 

  7. K. Bar-Eli,J. Phys. Chem.,94, 2368 (1990).

    Google Scholar 

  8. I. Schreiber and M. Marek,Phys. Lett.,91, 263 (1982).

    Google Scholar 

  9. P. S. Landa,Self-Oscillations in Systems with Many Degrees of Freedom [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  10. F. Growley and I. Epstein,J. Phys. Chem.,93, 2496 (1989).

    Google Scholar 

  11. M. Kawato M. and R. Suzuki,J. Theor. Biol.,86, 546 (1980).

    Google Scholar 

  12. D. G. Aronson, E. J. Doudel, and H. G. Othmer,Physica,25D, 20 (1987).

    Google Scholar 

  13. D. G. Aronson, G. B. Ermentrout, and N. Kopell,Physica,41D, 403 (1990).

    Google Scholar 

  14. E. I. Volkov and T. B. Pertsova,Kratk. Soobshch. Fiz., Phys. Inst. Akad. Nauk.11, 48 (1987).

    Google Scholar 

  15. E. I. Volkow (Volkov) and M. N. Stolyarov,Phys. Lett., bf 159A, 61 (1991).

    Google Scholar 

  16. G. Nikolis and I. Prigogine,Self-Organization in Non-Equilibrium Systems [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  17. E. G. Doedel, H. G. Kelker, and J. P. Kernevez,Int. J. Bifurc. Chaos,3, 493 (1991).

    Google Scholar 

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Authors
  1. E. I. Volkov
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  2. V. A. Romanov
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Additional information

P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 5, pp. 373–401, May, 1995.

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Volkov, E.I., Romanov, V.A. Bifurcations in a system of two identical diffusion-coupled relaxational brusselators. Radiophys Quantum Electron 38, 241–259 (1995). https://doi.org/10.1007/BF01038856

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  • DOI: https://doi.org/10.1007/BF01038856

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