Bifurcations of the periodic solutions in symmetric systems

Alois Klíč

Aplikace matematiky (1986)

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

Abstract

top
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

top

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

top
  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) MR0426007
  3. A. Klíč, Period doubling bifurcations in a two-box model of the Brusselator, Aplikace matematiky 5, sv. 28, 1983, 335-343. (1983) MR0712910
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.