Local and Global Bifurcations

2017 ◽  
pp. 209-230
Author(s):  
Stephen Lynch
Keyword(s):  
Global Bifurcations ◽  
Local And Global Bifurcations

scholarly journals Bifurcations of Nonconstant Solutions of the Ginzburg-Landau Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Norimichi Hirano ◽  
Sławomir Rybicki
Keyword(s):  
Landau Equation ◽  
Conley Index ◽  
Global Bifurcations ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Local And Global Bifurcations

We study local and global bifurcations of nonconstant solutions of the Ginzburg-Landau equation from the families of constant ones. As the topological tools we use the equivariant Conley index and the degree for equivariant gradient maps.

Codimension ${\bi n}$ flips

1998 ◽  
Vol 18 (5) ◽  
pp. 1115-1137 ◽  
Author(s):  
JAQUES GHEINER
Keyword(s):  
Global Bifurcations ◽  
Local And Global Bifurcations

The generic unfolding of codimension $n$ flips (one eigenvalue $-1$ and the others with norm different from 1) embedded in a Morse–Smale diffeomorphism is analyzed. Local and global bifurcations are described.

Response Scenario and Nonsmooth Features in the Nonlinear Dynamics of an Impacting Inverted Pendulum

2005 ◽  
Vol 1 (1) ◽  
pp. 56-64 ◽  
Author(s):  
Stefano Lenci ◽  
Lucio Demeio ◽  
Milena Petrini
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Investigation ◽  
Inverted Pendulum ◽  
Numerical Results ◽  
Dynamical Response ◽  
Global Bifurcations ◽  
Bifurcation Diagrams ◽  
Local And Global Bifurcations ◽  
And Behavior

In this work, we perform a systematic numerical investigation of the nonlinear dynamics of an inverted pendulum between lateral rebounding barriers. Three different families of considerably variable attractors—periodic, chaotic, and rest positions with subsequent chattering—are found. All of them are investigated, in detail, and the response scenario is determined by both bifurcation diagrams and behavior charts of single attractors, and overall maps. Attention is focused on local and global bifurcations that lead to the attractor-basin metamorphoses. Numerical results show the extreme richness of the dynamical response of the system, which is deemed to be of interest also in view of prospective mechanical applications.

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