Period doubling bifurcations in a two-box model of the Brusselator
Applications of Mathematics, Tome 28 (1983) no. 5, pp. 335-343
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1983.104045
Classification : 34C05, 34C25, 37G99, 37N99, 58F22, 92A15
Keywords: invariant vector field; Poincaré mapping; rotation number; period doubling bifurcation
@article{10_21136_AM_1983_104045,
     author = {Kl{\'\i}\v{c}, Alois},
     title = {Period doubling bifurcations in a two-box model of the {Brusselator}},
     journal = {Applications of Mathematics},
     pages = {335--343},
     year = {1983},
     volume = {28},
     number = {5},
     doi = {10.21136/AM.1983.104045},
     mrnumber = {0712910},
     zbl = {0531.34030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104045/}
}
TY  - JOUR
AU  - Klíč, Alois
TI  - Period doubling bifurcations in a two-box model of the Brusselator
JO  - Applications of Mathematics
PY  - 1983
SP  - 335
EP  - 343
VL  - 28
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104045/
DO  - 10.21136/AM.1983.104045
LA  - en
ID  - 10_21136_AM_1983_104045
ER  - 
%0 Journal Article
%A Klíč, Alois
%T Period doubling bifurcations in a two-box model of the Brusselator
%J Applications of Mathematics
%D 1983
%P 335-343
%V 28
%N 5
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104045/
%R 10.21136/AM.1983.104045
%G en
%F 10_21136_AM_1983_104045
Klíč, Alois. Period doubling bifurcations in a two-box model of the Brusselator. Applications of Mathematics, Tome 28 (1983) no. 5, pp. 335-343. doi: 10.21136/AM.1983.104045

[1] R. Lefevre: Stabilité des Structures Dissipatives. Bull. Classe Sci., Acad. Roy. Belgique, 54, 1968, 712.

[2] P. Glansdorff I. Prigogine: Thermodynamic Theory of Structure, Stability and Fluctuations. Wiley-Interscience, New York, 1971.

[3] J. J. Tyson: Some further studies of nonlinear oscillations in chemical systems. J. of Chemical Physics, Vol. 18, No. 9, 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. | DOI

[5] V. I. Arnold: Дополнительные главы теории обыкновенных дифференциальных уравнений. Nauka, Moskva, 1978. | MR | Zbl

[6] W. M. Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry. Academic Press, New York, 1975. | MR | Zbl

[7] J. E. Marsden M. McCracken: The Hopf Bifurcation and Its Applications. Springer-Verlag, New York, 1976. | MR

[8] D. Ruelle: Bifurcation in the presence of a symmetry group. Arch. Rat. Mech. An., 51, 1973, 136-152. | DOI | MR

[9] I. Schreiber M. Marek: Transition to chaos via two-torus in coupled reaction-diffusion cells. Physics Letters, Vol. 91, No. 6, 1982, p. 263. | DOI | MR

[10] I. Schreiber M. Marek: Strange attractors in coupled reaction-diffusion cells. Physica 5D, 1982, 258-272. | MR

[11] M. Kawato R. Suzuki: Two Coupled Neural Oscillators as a Model of Circadian Pacemaker. J. Theor. Biology, 1980, 86, 547-575. | DOI | MR

Cité par Sources :