| Title:
|
Period doubling bifurcations in a two-box model of the Brusselator (English) |
| Author:
|
Klíč, Alois |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
28 |
| Issue:
|
5 |
| Year:
|
1983 |
| Pages:
|
335-343 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
invariant vector field |
| Keyword:
|
Poincaré mapping |
| Keyword:
|
rotation number |
| Keyword:
|
period doubling bifurcation |
| MSC:
|
34C05 |
| MSC:
|
34C25 |
| MSC:
|
37G99 |
| MSC:
|
37N99 |
| MSC:
|
58F22 |
| MSC:
|
92A15 |
| idZBL:
|
Zbl 0531.34030 |
| idMR:
|
MR0712910 |
| DOI:
|
10.21136/AM.1983.104045 |
| . |
| Date available:
|
2008-05-20T18:23:02Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104045 |
| . |
| Reference:
|
[1] R. Lefevre: Stabilité des Structures Dissipatives.Bull. Classe Sci., Acad. Roy. Belgique, 54, 1968, 712. |
| Reference:
|
[2] P. Glansdorff I. Prigogine: Thermodynamic Theory of Structure, Stability and Fluctuations.Wiley-Interscience, New York, 1971. |
| Reference:
|
[3] J. J. Tyson: Some further studies of nonlinear oscillations in chemical systems.J. of Chemical Physics, Vol. 18, No. 9, 1973. |
| Reference:
|
[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. 10.1515/jnet.1979.4.2.93 |
| Reference:
|
[5] V. I. Arnold: Дополнительные главы теории обыкновенных дифференциальных уравнений.Nauka, Moskva, 1978. Zbl 0486.68013, MR 0526218 |
| Reference:
|
[6] W. M. Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry.Academic Press, New York, 1975. Zbl 0333.53001, MR 0426007 |
| Reference:
|
[7] J. E. Marsden M. McCracken: The Hopf Bifurcation and Its Applications.Springer-Verlag, New York, 1976. MR 0494309 |
| Reference:
|
[8] D. Ruelle: Bifurcation in the presence of a symmetry group.Arch. Rat. Mech. An., 51, 1973, 136-152. MR 0348796, 10.1007/BF00247751 |
| Reference:
|
[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. MR 0675223, 10.1016/0375-9601(82)90566-7 |
| Reference:
|
[10] I. Schreiber M. Marek: Strange attractors in coupled reaction-diffusion cells.Physica 5D, 1982, 258-272. MR 0680563 |
| Reference:
|
[11] M. Kawato R. Suzuki: Two Coupled Neural Oscillators as a Model of Circadian Pacemaker.J. Theor. Biology, 1980, 86, 547-575. MR 0610391, 10.1016/0022-5193(80)90352-5 |
| . |
