Bifurcations of the periodic solutions in symmetric systems

Alois Klíč

Aplikace matematiky (1986)

  • Volume: 31, Issue: 1, page 27-40
  • ISSN: 0862-7940

Abstract

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Bifurcation phenomena in systems of ordinary differential equations which are invariant with respect to involutive diffeomorphisms, are studied. Teh "symmetry-breaking" bifurcation is investigated in detail.

How to cite

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Klíč, Alois. "Bifurcations of the periodic solutions in symmetric systems." Aplikace matematiky 31.1 (1986): 27-40. <http://eudml.org/doc/15433>.

@article{Klíč1986,
abstract = {Bifurcation phenomena in systems of ordinary differential equations which are invariant with respect to involutive diffeomorphisms, are studied. Teh "symmetry-breaking" bifurcation is investigated in detail.},
author = {Klíč, Alois},
journal = {Aplikace matematiky},
keywords = {first order differential equation; delta-symmetric solution; periodic doubling bifurcations; symmetry-breaking bifurcations; first order differential equation; delta-symmetric solution; periodic doubling bifurcations; symmetry-breaking bifurcations},
language = {eng},
number = {1},
pages = {27-40},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bifurcations of the periodic solutions in symmetric systems},
url = {http://eudml.org/doc/15433},
volume = {31},
year = {1986},
}

TY - JOUR
AU - Klíč, Alois
TI - Bifurcations of the periodic solutions in symmetric systems
JO - Aplikace matematiky
PY - 1986
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 31
IS - 1
SP - 27
EP - 40
AB - Bifurcation phenomena in systems of ordinary differential equations which are invariant with respect to involutive diffeomorphisms, are studied. Teh "symmetry-breaking" bifurcation is investigated in detail.
LA - eng
KW - first order differential equation; delta-symmetric solution; periodic doubling bifurcations; symmetry-breaking bifurcations; first order differential equation; delta-symmetric solution; periodic doubling bifurcations; symmetry-breaking bifurcations
UR - http://eudml.org/doc/15433
ER -

References

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  1. V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag: New York, Heidelberg, Berlin, 1982. (Russian original, Moscow, 1978.) (1982) 
  2. W. M. Boothby, An Introduction to Difterentiable Manifolds and Riemannian Geometry, New York, Academic Press, 1975. (1975) Zbl0333.53001MR0426007
  3. A. Klíč, Period doubling bifurcations in a two-box model of the Brusselator, Aplikace matematiky 5, sv. 28, 1983, 335-343. (1983) Zbl0531.34030MR0712910
  4. J. W. Swift K. Wiesenfeld, Suppression of Period Doubling in Symmetric Systems, (unpublished). 
  5. J. W. Swift K. Wiesenfeld, 10.1103/PhysRevLett.52.705, Physical Review Letters, Vol. 52, No 9, 1984, 705-708. (1984) MR0734140DOI10.1103/PhysRevLett.52.705
  6. M. Field, 10.1090/S0002-9904-1970-12657-X, Bull. AMS 76, 1970, 1314-1318. (1970) Zbl0205.28204MR0277850DOI10.1090/S0002-9904-1970-12657-X
  7. J. E. Marsden M. McCrocken, The Hopf Bifurcation and Its Applications, New York, Springer-Verlag, 1976. (1976) MR0494309

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