# Bifurcations of the periodic solutions in symmetric systems

Aplikace matematiky (1986)

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

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topKlíč, 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

top- V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag: New York, Heidelberg, Berlin, 1982. (Russian original, Moscow, 1978.) (1982)
- W. M. Boothby, An Introduction to Difterentiable Manifolds and Riemannian Geometry, New York, Academic Press, 1975. (1975) Zbl0333.53001MR0426007
- A. Klíč, Period doubling bifurcations in a two-box model of the Brusselator, Aplikace matematiky 5, sv. 28, 1983, 335-343. (1983) Zbl0531.34030MR0712910
- J. W. Swift K. Wiesenfeld, Suppression of Period Doubling in Symmetric Systems, (unpublished).
- 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
- M. Field, 10.1090/S0002-9904-1970-12657-X, Bull. AMS 76, 1970, 1314-1318. (1970) Zbl0205.28204MR0277850DOI10.1090/S0002-9904-1970-12657-X
- J. E. Marsden M. McCrocken, The Hopf Bifurcation and Its Applications, New York, Springer-Verlag, 1976. (1976) MR0494309

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