Bifurcations of the periodic solutions in symmetric systems

Alois Klíč

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Period doubling bifurcations in a two-box model of the Brusselator

Alois Klíč (1983)

Aplikace matematiky

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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.

Period-doublings and orbit-bifurcations in symmetric systems

A. Vanderbauwhede (1989)

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Hopf bifurcation in symmetric systems

André L. Vanderbauwhede (1986)

Archivum Mathematicum

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Lie-point symmetries in bifurcation problems

G. Cicogna, G. Gaeta (1992)

Annales de l'I.H.P. Physique théorique

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One-Parameter Bifurcation Analysis of Dynamical Systems using Maple

Borisov, Milen, Dimitrova, Neli (2010)

Serdica Journal of Computing

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This paper presents two algorithms for one-parameter local bifurcations of equilibrium points of dynamical systems. The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities. * This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02–359/2008.

Breaking the continuity of a piecewise linear map

Viktor Avrutin, Michael Schanz, Björn Schenke (2012)

ESAIM: Proceedings

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Knowledge about the behavior of discontinuous piecewise-linear maps is important for a wide range of applications. An efficient way to investigate the bifurcation structure in 2D parameter spaces of such maps is to detect specific codimension-2 bifurcation points, called organizing centers, and to describe the bifurcation structure in their neighborhood. In this work, we present the organizing centers in the 1D discontinuous piecewise-linear...