Article
MSC:
34C05,
34C25,
37G99,
37N99,
58F22,
92A15 | MR 0712910 | Zbl 0531.34030 | DOI: 10.21136/AM.1983.104045
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Keywords:
invariant vector field; Poincaré mapping; rotation number; period doubling bifurcation
invariant vector field; Poincaré mapping; rotation number; period doubling bifurcation
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.
References:
[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 10.1515/jnet.1979.4.2.93
[5] V. I. Arnold: Дополнительные главы теории обыкновенных дифференциальных уравнений. Nauka, Moskva, 1978. MR 0526218 | Zbl 0486.68013
[6] W. M. Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry. Academic Press, New York, 1975. MR 0426007 | Zbl 0333.53001
[7] J. E. Marsden M. McCracken: The Hopf Bifurcation and Its Applications. Springer-Verlag, New York, 1976. MR 0494309
[8] D. Ruelle: Bifurcation in the presence of a symmetry group. Arch. Rat. Mech. An., 51, 1973, 136-152. DOI 10.1007/BF00247751 | MR 0348796
[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 10.1016/0375-9601(82)90566-7 | MR 0675223
[10] I. Schreiber M. Marek: Strange attractors in coupled reaction-diffusion cells. Physica 5D, 1982, 258-272. MR 0680563
[11] M. Kawato R. Suzuki: Two Coupled Neural Oscillators as a Model of Circadian Pacemaker. J. Theor. Biology, 1980, 86, 547-575. DOI 10.1016/0022-5193(80)90352-5 | MR 0610391
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