scholarly journals A remark on bifurcation of Fredholm maps

2018 ◽  
Vol 7 (3) ◽  
pp. 285-292 ◽  
Author(s):  
Nils Waterstraat
Keyword(s):  
Differential Equations ◽  
Bifurcation Set ◽  
Multiparameter Bifurcation ◽  
Fredholm Maps

AbstractWe modify an argument for multiparameter bifurcation of Fredholm maps by Fitzpatrick and Pejsachowicz to strengthen results on the topology of the bifurcation set. Furthermore, we discuss an application to families of differential equations parametrised by Grassmannians.

scholarly journals Basin explosions and escape phenomena in the twin-well Duffing oscillator: compound global bifurcations organizing behaviour

1990 ◽  
Vol 332 (1624) ◽  
pp. 169-186 ◽  
Keyword(s):  
Nonlinear Dynamics ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Duffing Oscillator ◽  
Potential Well ◽  
Global Bifurcations ◽  
Fractal Basin Boundaries ◽  
Codimension Two ◽  
Bifurcation Set ◽  
Basin Boundaries

The sinusoidally drive, twin-well Duffing oscillator has become a central archetypal model for studies of chaos and fractal basin boundaries in the nonlinear dynamics of dissipative ordinary differential equations. It can also be used to illustrate and elucidate universal features of the escape from a potential well, the jumps from one-well to cross-well motions displaying similar characteristics to those recently charted for the cubic one-well potential. We identify here some new codimension-two global bifurcations which serve to organize the bifurcation set and structure the related basin explosions and escape phenomena.

Sign in / Sign up

Export Citation Format

Share Document