main science this page only

Critical behavior associated with quasiperiodicity at the golden-mean frequency ratio

TCT - Torus Collision Terminal

alphabet


Description

This type of critical behavior occurs in two-parameter analysis of 1D map quasiperiodically forced with the golden-mean frequency. The critical point is located at the end of the torus-collision bifurcation curve.

 

RG equation:

 

The fixed point of the RG equation
g(x,y) =…


show enlarged figure

 

The orbital scaling factors

 

Relevant eigenvalues

 

Codimension
CoDim=2
(For 1D map, and, presumably, for more general systems too)

Examples: (1) Forced logistic map

Attractor scaling with


show enlarged figure

(2) Forced supercritical circle map

Parameter space arrangement

Scaling coordinates

(scaling with )


show enlarged figure


show enlarged figure

main science alphabet this page only top

Saratov group
of theoretical nonlinear
dynamics
Хостинг от uCoz