scholarly journals Period-doubling/symmetry-breaking mode interactions in iterated maps

2009 ◽  
Vol 238 (19) ◽  
pp. 1992-2002 ◽  
Author(s):  
P.J. Aston ◽  
H. Mir
Keyword(s):  
Symmetry Breaking ◽  
Period Doubling ◽  
Iterated Maps ◽  
Mode Interactions

Symmetry breaking and period doubling on a torus in the VLF regime in Taylor-Couette flow

1996 ◽  
Vol 54 (5) ◽  
pp. 4938-4957 ◽  
Author(s):  
J. von Stamm ◽  
U. Gerdts ◽  
Th. Buzug ◽  
G. Pfister
Keyword(s):  
Symmetry Breaking ◽  
Couette Flow ◽  
Period Doubling ◽  
Taylor Couette ◽  
Taylor Couette Flow

PERIOD-DOUBLING SCENARIO WITHOUT FLIP BIFURCATIONS IN A ONE-DIMENSIONAL MAP

2005 ◽  
Vol 15 (04) ◽  
pp. 1267-1284 ◽  
Author(s):  
V. AVRUTIN ◽  
M. SCHANZ
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Symmetry Breaking ◽  
Period Doubling ◽  
Pitchfork Bifurcation ◽  
Period Doubling Bifurcation ◽  
Coexisting Attractors ◽  
One Dimensional ◽  
Poincaré Return Map ◽  
Smooth Dynamical System

In this work a one-dimensional piecewise-smooth dynamical system, representing a Poincaré return map for dynamical systems of the Lorenz type, is investigated. The system shows a bifurcation scenario similar to the classical period-doubling one, but which is influenced by so-called border collision phenomena and denoted as border collision period-doubling bifurcation scenario. This scenario is formed by a sequence of pairs of bifurcations, whereby each pair consists of a border collision bifurcation and a pitchfork bifurcation. The mechanism leading to this scenario and its characteristic properties, like symmetry-breaking and symmetry-recovering as well as emergence of coexisting attractors, are investigated.

GROUP THEORETICAL MODE INTERACTIONS WITH DIFFERENT SYMMETRIES

1994 ◽  
Vol 04 (01) ◽  
pp. 177-191 ◽  
Author(s):  
KARIN GATERMANN ◽  
BODO WERNER
Keyword(s):  
Group Theory ◽  
Symmetry Breaking ◽  
Irreducible Representations ◽  
Bifurcation Points ◽  
Mode Interactions ◽  
Different Types ◽  
Secondary Bifurcation ◽  
Two Parameter ◽  
Symmetry Breaking Bifurcation

In two-parameter systems two symmetry breaking bifurcation points of different types coalesce generically within one point. This causes secondary bifurcation points to exist. The aim of this paper is to understand this phenomenon with group theory and the inner-connectivity of irreducible representations of supergroup and subgroups. Colored pictures of examples are included.

ROBUST METHOD FOR EXPERIMENTAL BIFURCATION ANALYSIS

2002 ◽  
Vol 12 (08) ◽  
pp. 1909-1913 ◽  
Author(s):  
GERRIT LANGER ◽  
ULRICH PARLITZ
Keyword(s):  
Symmetry Breaking ◽  
Bifurcation Analysis ◽  
Duffing Oscillator ◽  
Period Doubling ◽  
Robust Method ◽  
Periodically Driven ◽  
Experimental Systems ◽  
Saddle Node ◽  
Electronic Implementation

We present a robust method to locate and continue period-doubling, saddle-node and symmetry-breaking bifurcations of periodically driven experimental systems. The method is illustrated from results obtained for an electronic implementation of a Duffing oscillator.

scholarly journals Period-doubling cascades and mode interactions in coupled systems

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2030005-2030006
Author(s):  
P. J. Aston ◽  
H. Mir
Keyword(s):  
Period Doubling ◽  
Coupled Systems ◽  
Mode Interactions

scholarly journals Small-signal amplification of period-doubling bifurcations in smooth iterated maps

2006 ◽  
Vol 48 (4) ◽  
pp. 381-389 ◽  
Author(s):  
Xiaopeng Zhao ◽  
David G. Schaeffer ◽  
Carolyn M. Berger ◽  
Daniel J. Gauthier
Keyword(s):  
Signal Amplification ◽  
Period Doubling ◽  
Small Signal ◽  
Iterated Maps ◽  
Period Doubling Bifurcations

Numerical Methods for Steady State/Hopf Mode Interactions

1997 ◽  
Vol 07 (03) ◽  
pp. 585-605 ◽  
Author(s):  
F. Amdjadi ◽  
P. J. Aston
Keyword(s):  
Steady State ◽  
Numerical Methods ◽  
Symmetry Breaking ◽  
Mode Interaction ◽  
Extended System ◽  
Test Function ◽  
Alternative Approach ◽  
Mode Interactions ◽  
Sivashinsky Equation ◽  
Two Parameter

Numerical methods for dealing with steady state/Hopf mode interactions using extended systems are considered. In particular, it is shown that such a mode interaction corresponds to a symmetry breaking bifurcation of a Hopf extended system as well as a Hopf bifurcation of a symmetry breaking extended system. Non-degeneracy conditions associated with these bifurcations are derived and interpreted in the context of the mode interaction. The alternative approach of using a single test function instead of a full extended system is considered in detail in one of the cases. Numerical results for a two-parameter version of the Kuramoto–Sivashinsky equation are presented to illustrate the theory.

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