scholarly journals Asymptotic transversality and symmetry breaking bifurcation from boundary concentrating solutions

2012 ◽  
Vol 29 (1) ◽  
pp. 59-81 ◽  
Author(s):  
Yasuhito Miyamoto
Keyword(s):  
Symmetry Breaking ◽  
Concentrating Solutions ◽  
Symmetry Breaking Bifurcation

Amplitude Modulation and Symmetry Breaking Bifurcation in Micro Devices

2012 ◽  
Author(s):  
Z. C. Feng ◽  
Mahmoud Almasri
Keyword(s):  
Symmetry Breaking ◽  
Numerical Simulations ◽  
Amplitude Modulation ◽  
Dynamic Responses ◽  
Symmetric Structure ◽  
Different Types ◽  
Asymmetric Responses ◽  
Symmetric Response ◽  
Symmetry Breaking Bifurcation

Designs of many micro devices take advantage of the symmetry for better performance, immunity to noise, and for simpler analysis. When a symmetric structure is subjected to symmetric forcing, the symmetric response can become unstable leading to asymmetric responses. The occurrence of symmetry breaking bifurcation leads to complicated dynamic responses which often result in less desirable performances. In this paper, we obtain analytical criteria for the onset of symmetry breaking bifurcations. We also conduct numerical simulations to demonstrate different types of asymmetric dynamic responses resulting from the symmetry breaking bifurcation. In particular, we show the occurrence of amplitude modulated motions in such systems.

Symmetry-breaking bifurcation for the one-dimensional Hénon equation

2019 ◽  
Vol 21 (01) ◽  
pp. 1750097
Author(s):  
Inbo Sim ◽  
Satoshi Tanaka
Keyword(s):  
Symmetry Breaking ◽  
Bifurcation Point ◽  
Global Bifurcation ◽  
One Dimensional ◽  
Bifurcation Points ◽  
Connected Set ◽  
Hénon Equation ◽  
The One ◽  
Symmetry Breaking Bifurcation

We show the existence of a symmetry-breaking bifurcation point for the one-dimensional Hénon equation [Formula: see text] where [Formula: see text] and [Formula: see text]. Moreover, employing a variant of Rabinowitz’s global bifurcation, we obtain the unbounded connected set (the first of the alternatives about Rabinowitz’s global bifurcation), which emanates from the symmetry-breaking bifurcation point. Finally, we give an example of a bounded branch connecting two symmetry-breaking bifurcation points (the second of the alternatives about Rabinowitz’s global bifurcation) for the problem [Formula: see text] where [Formula: see text] is a specified continuous parametrization function.

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.

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