Period doubling bifurcations in a two-box model of the Brusselator

Alois Klíč

Aplikace matematiky (1983)

  • Volume: 28, Issue: 5, page 335-343
  • ISSN: 0862-7940

Abstract

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Two theorems about period doubling bifurcations are proved. A special case, where one multiplier of the homogeneous solution is equal to +1 is discussed in the Appendix.

How to cite

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Klíč, Alois. "Period doubling bifurcations in a two-box model of the Brusselator." Aplikace matematiky 28.5 (1983): 335-343. <http://eudml.org/doc/15313>.

@article{Klíč1983,
abstract = {Two theorems about period doubling bifurcations are proved. A special case, where one multiplier of the homogeneous solution is equal to +1 is discussed in the Appendix.},
author = {Klíč, Alois},
journal = {Aplikace matematiky},
keywords = {invariant vector field; Poincaré mapping; rotation number; period doubling bifurcation; invariant vector field; Poincaré mapping; rotation number; period doubling bifurcation},
language = {eng},
number = {5},
pages = {335-343},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Period doubling bifurcations in a two-box model of the Brusselator},
url = {http://eudml.org/doc/15313},
volume = {28},
year = {1983},
}

TY - JOUR
AU - Klíč, Alois
TI - Period doubling bifurcations in a two-box model of the Brusselator
JO - Aplikace matematiky
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 5
SP - 335
EP - 343
AB - Two theorems about period doubling bifurcations are proved. A special case, where one multiplier of the homogeneous solution is equal to +1 is discussed in the Appendix.
LA - eng
KW - invariant vector field; Poincaré mapping; rotation number; period doubling bifurcation; invariant vector field; Poincaré mapping; rotation number; period doubling bifurcation
UR - http://eudml.org/doc/15313
ER -

References

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  3. J. J. Tyson, Some further studies of nonlinear oscillations in chemical systems, J. of Chemical Physics, Vol. 18, No. 9, 1973. (1973) 
  4. G. Jetschke, Multiple Stable Steady States and Chemical Hysteresis in a Two-Box Model of the Brusselator, J. Non-Equilib. Thermodyn., Vol. 4, 1979, No. 2. (1979) 
  5. V. I. Arnold, Дополнительные главы теории обыкновенных дифференциальных уравнений, Nauka, Moskva, 1978. (1978) Zbl0486.68013MR0526218
  6. W. M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, Academic Press, New York, 1975. (1975) Zbl0333.53001MR0426007
  7. J. E. Marsden M. McCracken, The Hopf Bifurcation and Its Applications, Springer-Verlag, New York, 1976. (1976) MR0494309
  8. D. Ruelle, 10.1007/BF00247751, Arch. Rat. Mech. An., 51, 1973, 136-152. (1973) MR0348796DOI10.1007/BF00247751
  9. I. Schreiber M. Marek, 10.1016/0375-9601(82)90566-7, Physics Letters, Vol. 91, No. 6, 1982, p. 263. (1982) MR0675223DOI10.1016/0375-9601(82)90566-7
  10. I. Schreiber M. Marek, Strange attractors in coupled reaction-diffusion cells, Physica 5D, 1982, 258-272. (1982) MR0680563
  11. M. Kawato R. Suzuki, 10.1016/0022-5193(80)90352-5, J. Theor. Biology, 1980, 86, 547-575. (1980) MR0610391DOI10.1016/0022-5193(80)90352-5

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